Multiphase power supply with plural series connected cells and failed cell bypass

ABSTRACT

A high output level is maintained in power supplies having multiple cells in each leg. Failed cells in any leg are bypassed to provide a current path through the respective leg. All of the unfailed cells are utilized while maintaining equal magnitude between phases and a balance phase relationship in the line-to-line output voltage. The invention may be utilized in conjunction with a peak voltage reduction circuit, and a by-pass switch.

BACKGROUND OF THE INVENTION

I. Field of the Invention

This invention relates to a drive and specifically a drive and a methodfor operating a variable drive such as a variable-speed motor drivesystem.

II. Description of Prior Art

Variable-output drives traditionally are used in industry to providevariable electric power to AC motors. These same drives can be used inother applications not related specifically to motors but where avariable-output voltage or frequency is desired. Typical drives have anAC input power source and some type of conversion apparatus, usuallyusing solid-state devices, for converting the fixed AC input voltageinto a variable-voltage and/or variable-frequency output. One such typeof drive is described in U.S. Pat. No. 5,625,545, which is incorporatedherein by reference. That patent describes a power supply used as adrive which utilizes a number of power cells arranged to produce athree-phase AC output. Such multiple power cells in series can beutilized to provide higher voltage outputs than would be available withonly a single cell. However, should a given cell in a series arrangementfail during operation, that current path can become open-circuited,rendering the entire drive inoperable. In many applications, especiallyindustrial applications utilizing variable-speed drives, it is desirableto continue to operate in a reduced mode when a single cell fails. Onemethod to do such a reduced operation is to short out the damaged orfailed cell. This can then result in an unbalanced output, in that theleg having the shorted cell must operate at less than full voltage. Suchoperation can create imbalanced line conditions and be damaging to loadelements. Therefore, when a cell fails in a series arrangement, it isusually desirable to permit operation at a reduced voltage or speed byshunting out an equal number of cells in each of the other legs. Whilethe output from such a drive having shunted cells in each leg isreduced, it does permit the drive to operate at a reduced voltage orspeed. Often times such reduced operation is highly desirable so thatthe process being controlled by the drive can continue until it isconvenient to shut down for repairs. In addition, it may be desirable tooperate the drive at a reduced-voltage condition so as to maintain adesired minimum level of production. Typically, when a drive havingmultiple converters arranged in series has a failure, the output voltageand power available is reduced proportional to the ratio of the numberof unfailed cells in a given leg divided by the number of total cells insuch leg. As an example, if one of the cells in the aforesaid patent,such as power cell A₁ were to fail, typically power cells A₁, B₁ and C₁would be shunted by appropriate bypass circuitry. Such circuitry isshown in FIG. 9 of the U.S. Pat. No. 5,625,545. When operating undersuch bypass condition, the output of the three-phase drive at references22, 25 and 24 is proportionally reduced by one-third. In such anoperating condition, the output voltage available to the motor wouldonly be 66% of the full voltage. In such a condition, the motor wouldonly be able to reach approximately two-thirds of its rated speed. Inmany applications being able to reach even 66% of rated speed in afailed cell mode is desirable. However, it still represents asubstantial reduction in the output speed and power available from thedrive. When multiple power cells or converters are used in series, thetotal power delivered to the load is usually supplied generally equallyby all the power cells. Thus in the example above when one of nine cellsfails, 89% of rated power should still be available. By shunting out orbypassing two operational power cells such as B₁ and C₁ in the example,these power cells can no longer contribute to the output power availableto the load. It would be very desirable, then, to optimize the outputvoltage and power available to the load during a failed cell condition.The invention provides for an apparatus and a method that permitsoperation during a failed mode at a power output that utilizes all ofthe cells or converters that are operational.

SUMMARY OF THE INVENTION

The invention is directed to a method of operating a multiphase powersupply that has a plurality of cells or converters connected in seriesin each of a plurality of legs. This results in each leg having a legvoltage equal to the sum of connected cells in such leg. In addition,the power supply has a line-to-line voltage output between the terminalends of each pairs of legs. This invention applies to loads that are notconnected to the common leg junction, but only to the end points of thelegs, so that only the line-to-line output voltage appears on the load.During a failed condition in which any one or number of cells havefailed in any of the legs, the line-to-line voltage output is maximized.This is done by detecting failed cells in any of the legs and forming acurrent path around such failed cell by an electrical bypass. As aresult no voltage component from the failed cell is included within theleg in which it previously was connected. The outputs of the unfailedcells are controlled so as to maximize the line-to-line voltage in theoutput of the power supply so that their magnitudes are generally equal.By so regulating their outputs, the line-to-line phase voltages of theoutput of the power supply can be balanced. In a three-phase outputsupply without failed cells, balanced voltage is maintained by having a120° phase relationship between the leg output voltages. Theline-to-line phase balance can be restored by adjusting the leg-to-legphase relationship between the respective legs when failed cells aredetected. Circuitry is provided to implement a method for reducing thepeak voltage demands between legs. Voltage command signals can begenerated to provide peak voltage reduction, and such signals can bemodified to compensate for the detection of failed cells. Themodification can be a gain control using a gain which is proportional tothe ratio of the total number of cells in the leg (including failedcells) divided by the number of active cells (not bypassed) in the leg.The invention is particularly adapted to pulse width modulated serialconverters in each leg. The result is balanced line-to-line output fromthe power supply and full utilization of each unfailed cell in thesystem.

DESCRIPTION OF THE DRAWINGS

FIG. 1a is a diagram showing the power circuitry of an embodiment havingfive power cells in each leg of a three-phase drive.

FIG. 1b is a diagrammatic representation showing the converter circuitryof an embodiment of one cell such as those shown in FIG. 1a.

FIG. 1c is a diagrammatic representation of an embodiment of a controlsignal scheme that could be used to control a five-cell-per-leg drivesuch as shown in FIG. 1a.

FIG. 1d shows four alternative embodiments of a cell bypass.

FIG. 2 is a voltage diagram of a typical array of five cells connectedin series in each leg of a three-phase output.

FIG. 3 is a diagrammatic representation of voltage in an array similarto that shown in FIG. 2 but having two failed cells out of leg A.

FIG. 4 (Prior Art) is a voltage diagram showing a prior art method ofoperating with two failed cells in leg A and two cells removed from eachof leg B and C.

FIG. 5a is a voltage diagram of an array operating without two failedcells in leg A but utilizing all five cells in legs B and C.

FIG. 5b is a voltage diagram of an array operating after the loss of onecell in phase B and two cells in phase C.

FIG. 5c is a voltage diagram of an array operating after the loss of twocells in phase B and three cells in phase C.

FIG. 6 shows a diagram of a prior art control function to reduce thepeak voltage commands to a three-phase supply.

FIG. 7 shows a block diagram of a control function to reduce peakvoltage and to optimize the output voltage during operation with failedconverter cells.

FIG. 8a, b, c and d are diagrams showing control signal waveforms undervarious operating conditions.

FIG. 9a, b, c and d are signal waveforms of some embodiments.

FIG. 10a, b, c and d are control waveforms of some embodiments.

FIG. 11 is a circuit diagram of an embodiment of FIG. 7.

FIG. 12 shows a block diagram of a second improved control function toreduce peak voltage and optimize the output voltage during operationwith failed converter cells.

FIG. 13 is a diagram of a pneumatically operated transfer switch.

FIG. 14 is a transfer switch using a spring-loaded contact.

FIG. 15 is a diagram of a 3-cell arrangement using transfer switches.

DESCRIPTION OF SOME EMBODIMENTS

FIG. 1a shows a power circuit diagram for an AC drive. This is a typicalarrangement in which the invention can be utilized, however, otherdrives and power supplies can also utilize the apparatus and method ofthis invention. A three-phase incoming line 1 feeds into a powertransformer 2. As shown, power transformer 2 may be of anyconfiguration, and in some preferred embodiments will be the multiplewinding three-phase isolation transformer as shown in U.S. Pat. No.5,625,545. Such a transformer may have a primary winding which is staror mesh connected, which is energized from the three-phase incomingline 1. The transformer may then energize a number of single ormulti-phase secondary windings. In presently preferred embodiments,there will be a number of secondary windings each corresponding to arespective converter or power cell in the drive. It is also preferredthat the windings be preselected to certain degrees of electrical phasesuch as taught in the aforementioned patent. In some applications othertransformer configurations will be utilized, and in certain applicationsan incoming isolation transformer need not be utilized at all. As shownin FIG. 1a, the incoming transformer or other AC power supply feedsindividual power converters. In FIG. 1a, 15 power cells or convertersare utilized. In this circuit arrangement, there are three legs in theoutput line, each having five power converters. Leg A has converters A₁through A₅. Leg B contains power converters B₁ through B₅, and leg Ccontains power converters C₁ through C₅. The voltage available in anyleg is the result of the sum of the individual power cells in that leg,such that leg A has an output voltage which is the sum of powerconverters A₁ through A₅. Similarly, leg B has an output voltage whichis the sum of its converters, B₁ through B₅, and leg C has an outputvoltage which is the sum of the five converters arranged in series C₁through C₅. The drive feeds three-phase power to a motor 20, which maybe any load but in the diagram shown would commonly be an inductionmotor. This application is understood to produce a variable-speed ACdrive. As such, it may control process motors, fans, pumps or otherequipment. It is usually desirable to maintain a variable-speedoperation, either during an initial start-up or a process run. As such,the voltage available to the motor at terminals A, B and C is varied bycontrol of the drive. The motor 20 sees a voltage between terminals A-Bas the sum of the voltages of the individual power converters in leg Aand leg B. As a result, the motor voltage available at terminals A-Bequals the sum of the power cells (A₁ +A₂ +A₃ +A₄ +A₅ -B₁ -B₂ -B₃ -B₄-B₅). Respective other motor terminal voltages are also the summation ofthe voltages in the connections between their respective terminals. Assuch, the voltage between terminals B and C comprises the sum of thepower cells (B₁ +B₂ +B₃ +B₄ +B₅ -C₁ -C₂ -C₃ -C₄ -C₅). In a like mannerthe voltage from terminal C to A comprises the sum of the convertervoltages (C₁ +C₂ +C₃ +C₄ +C₅ -A₁ -A₂ -A₃ -A₄ -A₅). Each leg of the driveas shown is connected in a star having a common or neutral point N,which is not connected to the load, in this case motor 20. The outputvoltage component from each leg comprises the sum of the power cells inthe respective leg from the neutral to the motor terminal. Outputvoltage in leg A is measured between terminal A and N, the neutral pointof the converter arrangement. It includes the sum of the voltages onconverters A₁ through A₅. As can be seen if converter cell A₁ was tofail, the available voltage to the load, in this case motor 20, would bedecreased in the voltage measured from A to N, as one cell has beenremoved from that leg. If a drive is to be operated under this modewherein one of the cells has failed such as, for example, cell A₁, thatcell can be shorted or bypassed. To balance the output, typicallyanother cell in each of the other respective legs would also bebypassed. As an example, should cell A₁ fail, it is common practice tobypass cells A₁, B₁ and C₁. As a result, the output voltages availableto the motor terminals A, B and C would remain balanced. However, theavailable output voltage and output power would be reduced, because thenumber of active power cells being utilized in the circuitry has beenreduced. However, in practicing the present invention, should cell A₁fail, it can be bypassed and cells B and C can remain operational suchthat the output, voltage and power can be maintained at a higher maximumlevel.

FIG. 1b shows a typical power cell or converter such as A₁₋₅, B₁₋₅ andC₁₋₅, as shown in FIG. 1a. However, it is to be understood that otherpower cells or power converters can be utilized in practicing thisinvention. The power cell and control shown in FIG. 1b is similar tothat shown in U.S. Pat. No. 5,625,545. However, the master controllerprovides for control of the individual power cell in a manner thatpermits high output operation during a failed mode. Power cell 50, asshown, is a power converter which converts the three-phase incomingpower into a DC component through utilization of a rectifier composed ofdiodes 51_(a) -51_(c) and 52_(a) -52_(c). The output of this rectifieris then directed across capacitors 53_(a) and 53_(b), which can providestorage and smoothing of the DC output. Capacitors 53_(a) and 53_(b) arerepresentative of a capacitor bank, and the precise amount ofcapacitance necessary depends upon the specific application. The DCpower in the converter can be selectively applied to the converteroutputs 54 and 55 using a pulse-width modulated (PWM) method. Thepulse-width modulation may be implemented using a bridge converter whichis composed of semiconductor switches such as Q₁₋₄. Any type ofacceptable switch element can be used; and depending on the power level,various solid-state components may be chosen. As shown, the converteroutput utilizes four transistors 56, 57, 58 and 59. In such apulse-width modulated operation the switches can be considered eitherfully on or filly off as they operate. The circuit shown in FIG. 1b alsoutilizes four diodes 60-63 across each of the solid-state switch units.As will be understood in most applications, it is desirable that thepower cells or converters utilized in a multiconverter arrangement besimilar and constructed in a form so as to limit the number ofsubassemblies and permit converters to be interchangeable within thesame drive. Converter 50 as shown in FIG. 1b could be utilized for allof the 15 converters in FIG. 1a. Also shown as part of the powerconverter in FIG. 1b is a bypass 69. The bypass may also be constructedas an integral part of a converter subassembly in a drive unit. In otherapplications the bypass 69 can be separately mounted. The bypass 69 maybe mechanical, electrical or solid state. As presently preferred, thebypass unit utilized would be solid state and similar to that shown inFIG. 9 of U.S. Pat. No. 5,625,545. When bypass 69 is operated, it ineffect creates a shunt path between the respective output lines 54 and55 of the converter. As such, current can then be carried through thebypass 69 instead of the converter. If a failed converter which hasfailed in an open-circuit mode is not bypassed, the current through thatleg goes to zero. It is therefore desirable to have a bypass circuitsuch as 69 on each of the respective converter outputs. Many ways areknown as to monitoring and detecting a failed cell, and these may beused. A simple method is to compare cell output voltage to the commandedoutput. Other methods can include checking or verifying cell componentsor use of diagnostics routines. While the discussion of the inventionmay at times for simplicity imply that only a single cell fails, it isto be understood that the invention also covers apparatus and methodsutilized to permit continued operation with one or more cells havingfailed in a given leg or legs. As such, the invention can operate notonly when a single cell such as A₁ in FIG. 1a fails but would alsoprovide increased effective operation should multiple cells such as, forexample, A₁, B₂, B₃ and C₄ fail.

As shown in FIG. 1b, the converter is controlled through the utilizationof a local controller, such as shown at reference 65. It may bedesirable that the local controller also be associated with andcontained in the individual cell or converter. As such, it will controlthe specific converter, such as utilization of pulse-width modulation orother control techniques. The operation of the converter may be utilizedto control not only the output voltage but to control it in a mannerthat results in specific desired waveforms. The operation of the localcontroller may be operated as described in the previously referencedpatent. When the local controller is located on the individualconverter, it may be desirable that the control signals received fromthe master controller 67 are transmitted to the local controller throughutilization of a fiber optic system, such as for example a fiber opticcontrol link 66. It is to be understood that in practicing theinvention, certain control functions may be grouped together in themaster control such that a local controller is not necessary, and thatsignal transfer may be utilized in other means besides the utilizationof fiber optics, such as traditional wiring.

In instances where a local controller is contained in the individualpower cell subassembly, signals to that assembly may be generated from amaster controller. FIG. 1c shows a master controller 70, which isutilized to generate different signals V_(A) *, V_(B) * and V_(C) *.These signals V_(A) *, V_(B) * and V_(C) * are commands or replicas ofthe desired voltage output from the respective converters on Leg A, LegB, and Leg C. Master controller 70 feeds control signal V_(A) * to the Aleg converters A₁ through A₅, respectively. Similarly, the mastercontroller can control a signal, V_(B) *, to controllers B₁ through B₅.The master controller can also direct a signal to the third leg, C,through signal V_(C) * to converter C₁ through C₅. A PWM modulator canbe used to convert each voltage command into variable duty-cycleswitching patterns for the transistors 56, 57, 58, and 59 in FIG. 1b. Itis understood that the control scheme shown in FIG. 1c is only one ofmany control schemes that may be utilized in practicing the invention.

While prior practice in response to a failed cell has been to short outequal numbers of cells in all three phases, even though some of suchcells are still functional, the invention utilizes a method in which allfunctional cells can contribute to a balanced output voltage.

FIG. 1d shows some embodiments that alternatively may be used for bypassof a failed cell. Alternative i in FIG. 1d shows a power converter cellbeing bypassed by the contacts of a relay or contactor. When thecontact, shown in its open position is energized by the solenoid, ashunt path is created between the cell output terminals. An alternativebypass may be utilized as shown in ii. In this alternative, a triprelease device causes a spring loaded contact to provide a shunt pathbetween the cell output terminals. The trip release device may beelectrically or mechanically operated, and in some embodiments mayfunction as an open circuit detection device. iii shows a powerconverter which has across its output terminals a bypass circuitutilizing two silicon controlled rectifiers having reversed polarities.By turning on both SCRs a shunt path exists between the cell outputterminals. Depending upon the cost and specific application, a similarbypass may be constructed using series transistors as shown inalternative iv.

FIG. 2 shows a typical array of series-connected cells drawn toillustrate the voltage from each leg and the phase displacement betweenlegs. Each cell is capable of generating AC-output voltage of, forexample, 480 volts. Each cell is represented by a circle, with 5 cellsconnected in each leg between the neutral point N and the respectivepoints A, B and C. As shown, such an array can typically generate up toapproximately 2,400 volts from point N to each of points A, B and C. Ifthe control makes these three voltages equal in magnitude and mutuallyphase displaced by 120°, then the array will produce a balancedthree-phase AC output voltage. In this case the maximum availableline-to-line output voltage from the array shown in FIG. 2 can be 4,160volts. If one or more cells fail, it is possible to short-circuit thecell output terminals and continue operation at a reduced voltage. Theinactive cell or cells can be bypassed, as was described in FIG. 1b.

FIG. 3 shows the voltage available after cells A4 and A5 have beenbypassed. Because they have been bypassed, they do not show in thevoltage diagram in FIG. 3, as they do not contribute to the totalvoltage in the array. Bypassed cells A4 and A5 were in leg A, whichextends from N to point A. As shown in FIG. 3, only three cells, A1, A2and A3, now remain in the leg from N to A. This is because there is nocomponent of voltage remaining from the bypass cells. As a result, themaximum voltage available from leg A (between point N and point A) hasbeen reduced by 40% to approximately 1,440 volts. As shown, the fullvoltage is still available in the other legs from N to C and from N toB. If the control would continue to maintain the mutual-phasedisplacement angle at 120°, for example, then the output voltage will beunbalanced, as the voltage VCB would be much larger than the voltagesVAC and VBA. Such an unbalanced output voltage would be unsuitable fordriving a load such as a standard AC induction motor. To avoid thisundesirable condition and still maintain some operation of the load, ithas been a practice in prior art after one or more cells have failed tobypass the same number of cells in all three phases. Even though many ofthese cells are still fully functional, the desire to balance the outputvoltage to the load has exceeded the desire to use all available cells.In this condition the maximum output voltage from the entire array isthen limited to the capacity of the phase having the most failed cellsin a leg. The extra power capacity available in functional cells thathave been bypassed to maintain a balanced output is not utilized. FIG. 4shows the array of FIG. 3 after failed cells A4 and A5 have beenbypassed, and in addition, functional cells B4, B5, C4, and C5 have alsobeen bypassed. The maximum balanced line-to-line voltage in this figureis 60% of the rated voltage or, in the example, 2,494 volts. It isimportant to understand that the connection from the array of convertersor cells to the motor terminals normally consists of only three wires.The neutral point, N, of the array is usually not connected to theneutral of the motor. Therefore, it does not matter to the motor whetherthe leg voltages from point N to points A, B and C have the samemagnitude or even whether they are mutually phase-displaced by 120°. Themotor requires only that the line-to-line voltages VAC, VBA and VCB haveequal magnitude and are mutually phase-displaced by 120°. While thecircuitry of FIG. 4 provides balanced-output voltages and a phasedisplacement of 120°, it does not utilize the full capacity of all ofthe functional cells in the drive.

FIG. 5a shows how an array such as FIG. 1 could be configured afterfailure of cells A₄ and A₅. The figure assumes that cells A₄ and A₅,because of failure, have been bypassed and therefore have nocontribution from these cells to the overall voltage in leg A, thevoltage from N to A. The operation of the drive to achieve the voltagediagram in FIG. 5 utilizes a phase angle between phase B and C that hasbeen reduced from 120° to 95°. The remaining angles between A and C andbetween B and A have been increased from 120° to 132.5°. These anglesnow result in the line-to-line voltages VAC, VBA and VCB having equalmagnitudes. In addition, the mutual phase displacement in FIG. 5a is120° between VAC, VCB and VBA. The maximum balanced line-to-line voltagenow available as shown in FIG. 5 is 85% of the rated voltage, or 3,542volts. As the motor still experiences balance of the three-phasevoltages, it will continue to draw balanced three-phase currents, whichhave a mutual-phase displacement of 120°. However, since the cellvoltages no longer have a mutual-phase displacement of 120°, the anglebetween the cell voltage and the cell current may now vary among thephases. At light loads, when the motor current lags the motor voltage bynearly 90°, some of the cells may experience a cell current which lagsthe cell voltage by more than 90°. This can cause the cells to absorbenergy, which they may not be able to dissipate or regenerate.Therefore, it may be desirable to avoid operation in this manner underlight loads. Appropriate current or load-sensing can be implemented whenlight load operation of a drive utilizing this invention is desired.

FIG. 5b shows another example, where one cell has failed on Leg B (B5)and two have failed in Leg C (C4 and C5). Here the angle between A and Bhas been reduced to 96.9° while the angle between A and C has beenreduced to 113.1°. This again gives balanced line-to-line voltages of3249 volts, or 78% of rated.

FIG. 5c shows another examples where B4, B5, C3, C4 and C5 have all beenbypassed. The adjustment still allows 51% of voltage, or 2121 volts.

The control angles required will depend on the number of functionalcells remaining in each phase. The specific values for thephase-to-phase relationship can be calculated in the control as a failedcondition is detected. In other instances, it may be desirable to havepredetermined phase angles that represent given failure conditions.FIGS. 3, 5a, 5b and 5c show specific failure conditions. All of theseexamples utilize five cells per phase. It is obvious that other failedconditions can exist in the five cell per phase structure. In addition,the invention can be practiced utilizing any number of cells per phase.Once the number of cells utilized per phase in a given application isknown, such as for example, five cells per leg, the fault specifics canbe determined and appropriate leg-to-leg phase angle can be calculated.In lieu of calculating the specific leg-to-leg phase angle, it maydesirable to have certain fault conditions programmed into the system.These may be predetermined values for given fault situations. A lookuptable or tables can be utilized in practicing the invention. Tables 1-7which follows give general values of the leg-to-leg phase relationshipfor power supplies utilizing anywhere from two to eight cells per leg.In these tables, the legs are assumed to be in a three-phase Yarrangement having legs A, B and C. The table has been abbreviated inthat it gives the same values without regard to which cell in a givenleg fails. In addition, since a failure condition in a power supplyresults in identical phase relationships without regard to which legshave the number of failures, a power supply with A=5, B=3 and C=5, isthe same as a power supply having active cells A=5, B=5 and C=3. Thetable, therefore, provides an easy reduced form in which to cover all ofthese combinations. In the table, the A cell is always listed as havingthe most number of active cells, the B, second most number of activecells, and C the least number of active cells. Tables 1-7 could be usedin a microprocessor scheme as lookup tables to determine the properphase relationship in a power supply having failed cells. In the table,the term Vmax % is used to indicate the maximum voltage that would beavailable under a failed condition as a percentage of the normalline-to-line voltage. All of the phase angles are in relationship to thenormal A vector in a power supply having no failed cells. As an example,Aφ is the angle between the A leg in a failed mode as compared to the Aleg in an unfailed mode. All of the angles given are in relation to thevector for the A leg in an unfailed mode. Because the examples givenpreviously related to five cells per leg these examples can be seen inTable 4.

                                      TABLE 1                                     __________________________________________________________________________    Original number of cells = 2                                                  __________________________________________________________________________    A cells = 1                                                                         B cells = 1                                                                         C cells = 0                                                                         Vmax % = 28.9                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 1                                                                         B cells = 1                                                                         C cells = 1                                                                         Vmax % = 50.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 2                                                                         B cells = 1                                                                         C cells = 1                                                                         Vmax % = 50.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 60.0                                                                  C.sub..0.  = 300.0                        A cells = 2                                                                         B cells = 2                                                                         C cells = 0                                                                         Vmax % = 57.7                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 2                                                                         B cells = 2                                                                         C cells = 1                                                                         Vmax % = 80.9                                                                         A.sub..0.  = 15.5                                                                  B.sub..0.  = 104.5                                                                 C.sub..0.  = 240.0                        A cells = 2                                                                         B cells = 2                                                                         C cells = 2                                                                         Vmax % = 100.0                                                                        A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        __________________________________________________________________________

                                      TABLE 2                                     __________________________________________________________________________    Original number of cells = 3                                                  __________________________________________________________________________    A cells = 1                                                                         B cells = 1                                                                         C cells = 0                                                                         Vmax % = 19.2                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 1                                                                         B cells = 1                                                                         C cells = 1                                                                         Vmax % = 33.3                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 2                                                                         B cells = 1                                                                         C cells = 1                                                                         Vmax % = 33.3                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 60.0                                                                  C.sub..0.  = 300.0                        A cells = 2                                                                         B cells = 2                                                                         C cells = 0                                                                         Vmax % = 38.5                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 2                                                                         B cells = 2                                                                         C cells = 1                                                                         Vmax % = 53.9                                                                         A.sub..0.  = 15.5                                                                  B.sub..0.  = 104.5                                                                 C.sub..0.  = 240.0                        A cells = 2                                                                         B cells = 2                                                                         C cells = 2                                                                         Vmax % = 66.7                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 3                                                                         B cells = 2                                                                         C cells = 2                                                                         Vmax % = 75.5                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 101.4                                                                 C.sub..0.  = 258.6                        A cells = 3                                                                         B cells = 3                                                                         C cells = 0                                                                         Vmax % = 57.7                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 3                                                                         B cells = 3                                                                         C cells = 1                                                                         Vmax % = 73.6                                                                         A.sub..0.  = 20.4                                                                  B.sub..0.  = 99.6                                                                  C.sub..0.  = 240.0                        A cells = 3                                                                         B cells = 3                                                                         C cells = 2                                                                         Vmax % = 87.8                                                                         A.sub..0.  = 10.5                                                                  B.sub..0.  = 109.5                                                                 C.sub..0.  = 240.0                        A cells = 3                                                                         B cells = 3                                                                         C cells = 3                                                                         Vmax % = 100.0                                                                        A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        __________________________________________________________________________

                                      TABLE 3                                     __________________________________________________________________________    Original number of cells = 4                                                  __________________________________________________________________________    A cells = 1                                                                         B cells = 1                                                                         C cells = 0                                                                         Vmax % = 14.4                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 1                                                                         B cells = 1                                                                         C cells = 1                                                                         Vmax % = 25.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 2                                                                         B cells = 1                                                                         C cells = 1                                                                         Vmax % = 25.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 60.0                                                                  C.sub..0.  = 300.0                        A cells = 2                                                                         B cells = 2                                                                         C cells = 0                                                                         Vmax % = 28.9                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 2                                                                         B cells = 2                                                                         C cells = 1                                                                         Vmax % = 40.5                                                                         A.sub..0.  = 15.5                                                                  B.sub..0.  = 104.5                                                                 C.sub..0.  = 240.0                        A cells = 2                                                                         B cells = 2                                                                         C cells = 2                                                                         Vmax % = 50.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 3                                                                         B cells = 2                                                                         C cells = 2                                                                         Vmax % = 56.6                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 101.4                                                                 C.sub..0.  = 258.6                        A cells = 3                                                                         B cells = 3                                                                         C cells = 0                                                                         Vmax % = 43.3                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 3                                                                         B cells = 3                                                                         C cells = 1                                                                         Vmax % = 55.2                                                                         A.sub..0.  = 20.4                                                                  B.sub..0.  = 99.6                                                                  C.sub..0.  = 240.0                        A cells = 3                                                                         B cells = 3                                                                         C cells = 2                                                                         Vmax % = 65.8                                                                         A.sub..0.  = 10.5                                                                  B.sub..0.  = 109.5                                                                 C.sub..0.  = 240.0                        A cells = 3                                                                         B cells = 3                                                                         C cells = 3                                                                         Vmax % = 75.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 4                                                                         B cells = 2                                                                         C cells = 2                                                                         Vmax % = 50.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 60.0                                                                  C.sub..0.  = 300.0                        A cells = 4                                                                         B cells = 3                                                                         C cells = 1                                                                         Vmax % = 52.1                                                                         A.sub..0.  = 16.1                                                                  B.sub..0.  = 76.2                                                                  C.sub..0.  = 315.8                        A cells = 4                                                                         B cells = 3                                                                         C cells = 2                                                                         Vmax % = 71.5                                                                         A.sub..0.  = 7.2                                                                   B.sub..0.  = 96.2                                                                  C.sub..0.  = 260.7                        A cells = 4                                                                         B cells = 3                                                                         C cells = 3                                                                         Vmax % = 82.3                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 108.2                                                                 C.sub..0.  = 251.8                        A cells = 4                                                                         B cells = 4                                                                         C cells = 0                                                                         Vmax % = 57.7                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 4                                                                         B cells = 4                                                                         C cells = 1                                                                         Vmax % = 69.8                                                                         A.sub..0.  = 22.8                                                                  B.sub..0.  = 97.2                                                                  C.sub..0.  = 240.0                        A cells = 4                                                                         B cells = 4                                                                         C cells = 2                                                                         Vmax % = 80.9                                                                         A.sub..0.  = 15.5                                                                  B.sub..0.  = 104.5                                                                 C.sub..0.  = 240.0                        A cells = 4                                                                         B cells = 4                                                                         C cells = 3                                                                         Vmax % = 91.0                                                                         A.sub..0.  = 8.0                                                                   B.sub..0.  = 112.0                                                                 C.sub..0.  = 240.0                        A cells = 4                                                                         B cells = 4                                                                         C cells = 4                                                                         Vmax % = 100.0                                                                        A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        __________________________________________________________________________

                                      TABLE 4                                     __________________________________________________________________________    Original number of cells = 5                                                  __________________________________________________________________________    A cells = 1                                                                         B cells = 1                                                                         C cells = 0                                                                         Vmax % = 11.5                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 1                                                                         B cells = 1                                                                         C cells = 1                                                                         Vmax % = 20.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 2                                                                         B cells = 1                                                                         C cells = 1                                                                         Vmax % = 20.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 60.0                                                                  C.sub..0.  = 300.0                        A cells = 2                                                                         B cells = 2                                                                         C cells = 0                                                                         Vmax % = 23.1                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 2                                                                         B cells = 2                                                                         C cells = 1                                                                         Vmax % = 32.4                                                                         A.sub..0.  = 15.5                                                                  B.sub..0.  = 104.5                                                                 C.sub..0.  = 240.0                        A cells = 2                                                                         B cells = 2                                                                         C cells = 2                                                                         Vmax % = 40.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 3                                                                         B cells = 2                                                                         C cells = 2                                                                         Vmax % = 45.3                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 101.4                                                                 C.sub..0.  = 258.6                        A cells = 3                                                                         B cells = 3                                                                         C cells = 0                                                                         Vmax % = 34.6                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 3                                                                         B cells = 3                                                                         C cells = 1                                                                         Vmax % = 44.2                                                                         A.sub..0.  = 20.4                                                                  B.sub..0.  = 99.6                                                                  C.sub..0.  = 240.0                        A cells = 3                                                                         B cells = 3                                                                         C cells = 2                                                                         Vmax % = 52.7                                                                         A.sub..0.  = 10.5                                                                  B.sub..0.  = 109.5                                                                 C.sub..0.  = 240.0                        A cells = 3                                                                         B cells = 3                                                                         C cells = 3                                                                         Vmax % = 60.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 4                                                                         B cells = 2                                                                         C cells = 2                                                                         Vmax % = 40.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 60.0                                                                  C.sub..0.  = 300.0                        A cells = 4                                                                         B cells = 3                                                                         C cells = 1                                                                         Vmax % = 41.7                                                                         A.sub..0.  = 16.1                                                                  B.sub..0.  = 76.2                                                                  C.sub..0.  = 315.8                        A cells = 4                                                                         B cells = 3                                                                         C cells = 2                                                                         Vmax % = 57.2                                                                         A.sub..0.  = 7.2                                                                   B.sub..0.  = 96.2                                                                  C.sub..0.  = 260.7                        A cells = 4                                                                         B cells = 3                                                                         C cells = 3                                                                         Vmax % = 65.8                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 108.2                                                                 C.sub..0.  = 251.8                        A cells = 4                                                                         B cells = 4                                                                         C cells = 0                                                                         Vmax % = 46.2                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 4                                                                         B cells = 4                                                                         C cells = 1                                                                         Vmax % = 55.8                                                                         A.sub..0.  = 22.8                                                                  B.sub..0.  = 97.2                                                                  C.sub..0.  = 240.0                        A cells = 4                                                                         B cells = 4                                                                         C cells = 2                                                                         Vmax % = 64.7                                                                         A.sub..0.  = 15.5                                                                  B.sub..0.  = 104.5                                                                 C.sub..0.  = 240.0                        A cells = 4                                                                         B cells = 4                                                                         C cells = 3                                                                         Vmax % = 72.8                                                                         A.sub..0.  = 8.0                                                                   B.sub..0.  = 112.0                                                                 C.sub..0.  = 240.0                        A cells = 4                                                                         B cells = 4                                                                         C cells = 4                                                                         Vmax % = 80.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 5                                                                         B cells = 3                                                                         C cells = 2                                                                         Vmax % = 51.0                                                                         A.sub..0.  = 6.5                                                                   B.sub..0.  = 67.6                                                                  C.sub..0.  = 304.9                        A cells = 5                                                                         B cells = 3                                                                         C cells = 3                                                                         Vmax % = 69.1                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 93.6                                                                  C.sub..0.  = 266.4                        A cells = 5                                                                         B cells = 4                                                                         C cells = 1                                                                         Vmax % = 53.4                                                                         A.sub..0.  = 18.9                                                                  B.sub..0.  = 79.6                                                                  C.sub..0.  = 316.1                        A cells = 5                                                                         B cells = 4                                                                         C cells = 2                                                                         Vmax % = 69.0                                                                         A.sub..0.  = 11.6                                                                  B.sub..0.  = 93.9                                                                  C.sub..0.  = 262.1                        A cells = 5                                                                         B cells = 4                                                                         C cells = 3                                                                         Vmax % = 78.1                                                                         A.sub..0.  = 5.9                                                                   B.sub..0.  = 102.8                                                                 C.sub..0.  = 252.8                        A cells = 5                                                                         B cells = 4                                                                         C cells = 4                                                                         Vmax % = 86.1                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 111.3                                                                 C.sub..0.  = 248.7                        A cells = 5                                                                         B cells = 5                                                                         C cells = 0                                                                         Vmax % = 57.7                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 5                                                                         B cells = 5                                                                         C cells = 1                                                                         Vmax % = 67.4                                                                         A.sub..0.  = 24.3                                                                  B.sub..0.  = 95.7                                                                  C.sub..0.  = 240.0                        A cells = 5                                                                         B cells = 5                                                                         C cells = 2                                                                         Vmax % = 76.6                                                                         A.sub..0.  = 18.5                                                                  B.sub..0.  = 101.5                                                                 C.sub..0.  = 240.0                        A cells = 5                                                                         B cells = 5                                                                         C cells = 3                                                                         Vmax % = 85.1                                                                         A.sub..0.  = 12.5                                                                  B.sub..0.  = 107.5                                                                 C.sub..0.  = 240.0                        A cells = 5                                                                         B cells = 5                                                                         C cells = 4                                                                         Vmax % = 92.9                                                                         A.sub..0.  = 6.4                                                                   B.sub..0.  = 113.6                                                                 C.sub..0.  = 240.0                        A cells = 5                                                                         B cells = 5                                                                         C cells = 5                                                                         Vmax % = 100.0                                                                        A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        __________________________________________________________________________

                                      TABLE 5                                     __________________________________________________________________________    Original number of cells = 6                                                  __________________________________________________________________________    A cells = 1                                                                         B cells = 1                                                                         C cells = 0                                                                         Vmax % = 9.6                                                                          A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 1                                                                         B cells = 1                                                                         C cells = 1                                                                         Vmax % = 16.7                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 2                                                                         B cells = 1                                                                         C cells = 1                                                                         Vmax % = 16.7                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 60.0                                                                  C.sub..0.  = 300.0                        A cells = 2                                                                         B cells = 2                                                                         C cells = 0                                                                         Vmax % = 19.2                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 2                                                                         B cells = 2                                                                         C cells = 1                                                                         Vmax % = 27.0                                                                         A.sub..0.  = 15.5                                                                  B.sub..0.  = 104.5                                                                 C.sub..0.  = 240.0                        A cells = 2                                                                         B cells = 2                                                                         C cells = 2                                                                         Vmax % = 33.3                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 3                                                                         B cells = 2                                                                         C cells = 2                                                                         Vmax % = 37.7                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 101.4                                                                 C.sub..0.  = 258.6                        A cells = 3                                                                         B cells = 3                                                                         C cells = 0                                                                         Vmax % = 28.9                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 3                                                                         B cells = 3                                                                         C cells = 1                                                                         Vmax % = 36.8                                                                         A.sub..0.  = 20.4                                                                  B.sub..0.  = 99.6                                                                  C.sub..0.  = 240.0                        A cells = 3                                                                         B cells = 3                                                                         C cells = 2                                                                         Vmax % = 43.9                                                                         A.sub..0.  = 10.5                                                                  B.sub..0.  = 109.5                                                                 C.sub..0.  = 240.0                        A cells = 3                                                                         B cells = 3                                                                         C cells = 3                                                                         Vmax % = 50.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 4                                                                         B cells = 2                                                                         C cells = 2                                                                         Vmax % = 33.3                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 60.0                                                                  C.sub..0.  = 300.0                        A cells = 4                                                                         B cells = 3                                                                         C cells = 1                                                                         Vmax % = 34.7                                                                         A.sub..0.  = 16.1                                                                  B.sub..0.  = 76.2                                                                  C.sub..0.  = 315.8                        A cells = 4                                                                         B cells = 3                                                                         C cells = 2                                                                         Vmax % = 47.7                                                                         A.sub..0.  = 7.2                                                                   B.sub..0.  = 96.2                                                                  C.sub..0.  = 260.7                        A cells = 4                                                                         B cells = 3                                                                         C cells = 3                                                                         Vmax % = 54.9                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 108.2                                                                 C.sub..0.  = 251.8                        A cells = 4                                                                         B cells = 4                                                                         C cells = 0                                                                         Vmax % = 38.5                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 4                                                                         B cells = 4                                                                         C cells = 1                                                                         Vmax % = 46.5                                                                         A.sub..0.  = 22.8                                                                  B.sub..0.  = 97.2                                                                  C.sub..0.  = 240.0                        A cells = 4                                                                         B cells = 4                                                                         C cells = 2                                                                         Vmax % = 53.9                                                                         A.sub..0.  = 15.5                                                                  B.sub..0.  = 104.5                                                                 C.sub..0.  = 240.0                        A cells = 4                                                                         B cells = 4                                                                         C cells = 3                                                                         Vmax % = 60.7                                                                         A.sub..0.  = 8.0                                                                   B.sub..0.  = 112.0                                                                 C.sub..0.  = 240.0                        A cells = 4                                                                         B cells = 4                                                                         C cells = 4                                                                         Vmax % = 66.7                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 5                                                                         B cells = 3                                                                         C cells = 2                                                                         Vmax % = 42.5                                                                         A.sub..0.  = 6.5                                                                   B.sub..0.  = 67.6                                                                  C.sub..0.  = 304.9                        A cells = 5                                                                         B cells = 3                                                                         C cells = 3                                                                         Vmax % = 57.6                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 93.6                                                                  C.sub..0.  = 266.4                        A cells = 5                                                                         B cells = 4                                                                         C cells = 1                                                                         Vmax % = 44.5                                                                         A.sub..0.  = 18.9                                                                  B.sub..0.  = 79.6                                                                  C.sub..0.  = 316.1                        A cells = 5                                                                         B cells = 4                                                                         C cells = 2                                                                         Vmax % = 57.5                                                                         A.sub..0.  = 11.6                                                                  B.sub..0.  = 93.9                                                                  C.sub..0.  = 262.1                        A cells = 5                                                                         B cells = 4                                                                         C cells = 3                                                                         Vmax % = 65.1                                                                         A.sub..0.  = 5.9                                                                   B.sub..0.  = 102.8                                                                 C.sub..0.  = 252.8                        A cells = 5                                                                         B cells = 4                                                                         C cells = 4                                                                         Vmax % = 71.7                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 111.3                                                                 C.sub..0.  = 248.7                        A cells = 5                                                                         B cells = 5                                                                         C cells = 0                                                                         Vmax % = 48.1                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 5                                                                         B cells = 5                                                                         C cells = 1                                                                         Vmax % = 56.2                                                                         A.sub..0.  = 24.3                                                                  B.sub..0.  = 95.7                                                                  C.sub..0.  = 240.0                        A cells = 5                                                                         B cells = 5                                                                         C cells = 2                                                                         Vmax % = 63.8                                                                         A.sub..0.  = 18.5                                                                  B.sub..0.  = 101.5                                                                 C.sub..0.  = 240.0                        A cells = 5                                                                         B cells = 5                                                                         C cells = 3                                                                         Vmax % = 70.9                                                                         A.sub..0.  = 12.5                                                                  B.sub..0.  = 107.5                                                                 C.sub..0.  = 240.0                        A cells = 5                                                                         B cells = 5                                                                         C cells = 4                                                                         Vmax % = 77.4                                                                         A.sub..0.  = 6.4                                                                   B.sub..0.  = 113.6                                                                 C.sub..0.  = 240.0                        A cells = 5                                                                         B cells = 5                                                                         C cells = 5                                                                         Vmax % = 83.3                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 6                                                                         B cells = 3                                                                         C cells = 3                                                                         Vmax % = 50.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 60.0                                                                  C.sub..0.  = 300.0                        A cells = 6                                                                         B cells = 4                                                                         C cells = 3                                                                         Vmax % = 67.3                                                                         A.sub..0.  = 4.8                                                                   B.sub..0.  = 91.2                                                                  C.sub..0.  = 268.4                        A cells = 6                                                                         B cells = 4                                                                         C cells = 4                                                                         Vmax % = 75.5                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 101.4                                                                 C.sub..0.  = 258.6                        A cells = 6                                                                         B cells = 5                                                                         C cells = 1                                                                         Vmax % = 55.1                                                                         A.sub..0.  = 20.5                                                                  B.sub..0.  = 82.4                                                                  C.sub..0.  = 311.3                        A cells = 6                                                                         B cells = 5                                                                         C cells = 2                                                                         Vmax % = 67.2                                                                         A.sub..0.  = 14.5                                                                  B.sub..0.  = 92.7                                                                  C.sub..0.  = 263.2                        A cells = 6                                                                         B cells = 5                                                                         C cells = 3                                                                         Vmax % = 75.1                                                                         A.sub..0.  = 9.8                                                                   B.sub..0.  = 99.8                                                                  C.sub..0.  = 253.6                        A cells = 6                                                                         B cells = 5                                                                         C cells = 4                                                                         Vmax % = 82.1                                                                         A.sub..0.  = 5.0                                                                   B.sub..0.  = 106.5                                                                 C.sub..0.  = 249.3                        A cells = 6                                                                         B cells = 5                                                                         C cells = 5                                                                         Vmax % = 88.5                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 113.1                                                                 C.sub..0.  = 246.9                        A cells = 6                                                                         B cells = 6                                                                         C cells = 0                                                                         Vmax % = 57.7                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 6                                                                         B cells = 6                                                                         C cells = 1                                                                         Vmax % = 65.9                                                                         A.sub..0.  = 25.2                                                                  B.sub..0.  = 94.8                                                                  C.sub..0.  = 240.0                        A cells = 6                                                                         B cells = 6                                                                         C cells = 2                                                                         Vmax % = 73.6                                                                         A.sub..0.  = 20.4                                                                  B.sub..0.  = 99.6                                                                  C.sub..0.  = 240.0                        A cells = 6                                                                         B cells = 6                                                                         C cells = 3                                                                         Vmax % = 80.9                                                                         A.sub..0.  = 15.5                                                                  B.sub..0.  = 104.5                                                                 C.sub..0.  = 240.0                        A cells = 6                                                                         B cells = 6                                                                         C cells = 4                                                                         Vmax % = 87.8                                                                         A.sub..0.  = 10.5                                                                  B.sub..0.  = 109.5                                                                 C.sub..0.  = 240.0                        A cells = 6                                                                         B cells = 6                                                                         C cells = 5                                                                         Vmax % = 94.1                                                                         A.sub..0.  = 5.4                                                                   B.sub..0.  = 114.6                                                                 C.sub..0.  = 240.0                        A cells = 6                                                                         B cells = 6                                                                         C cells = 6                                                                         Vmax % = 100.0                                                                        A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        __________________________________________________________________________

                                      TABLE 6                                     __________________________________________________________________________    Original number of cells = 7                                                  __________________________________________________________________________    A cells = 1                                                                         B cells = 1                                                                         C cells = 0                                                                         Vmax % = 8.2                                                                          A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 1                                                                         B cells = 1                                                                         C cells = 1                                                                         Vmax % = 14.3                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 2                                                                         B cells = 1                                                                         C cells = 1                                                                         Vmax % = 14.3                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 60.0                                                                  C.sub..0.  = 300.0                        A cells = 2                                                                         B cells = 2                                                                         C cells = 0                                                                         Vmax % = 16.5                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 2                                                                         B cells = 2                                                                         C cells = 1                                                                         Vmax % = 23.1                                                                         A.sub..0.  = 15.5                                                                  B.sub..0.  = 104.5                                                                 C.sub..0.  = 240.0                        A cells = 2                                                                         B cells = 2                                                                         C cells = 2                                                                         Vmax % = 28.6                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 3                                                                         B cells = 2                                                                         C cells = 2                                                                         Vmax % = 32.3                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 101.4                                                                 C.sub..0.  = 258.6                        A cells = 3                                                                         B cells = 3                                                                         C cells = 0                                                                         Vmax % = 24.7                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 3                                                                         B cells = 3                                                                         C cclls = 1                                                                         Vmax % = 31.5                                                                         A.sub..0.  = 20.4                                                                  B.sub..0.  = 99.6                                                                  C.sub..0.  = 240.0                        A cells = 3                                                                         B cells = 3                                                                         C cells = 2                                                                         Vmax % = 37.6                                                                         A.sub..0.  = 10.5                                                                  B.sub..0.  = 109.5                                                                 C.sub..0.  = 240.0                        A cells = 3                                                                         B cells = 3                                                                         C cells = 3                                                                         Vmax % = 42.9                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 4                                                                         B cells = 2                                                                         C cells = 2                                                                         Vmax % = 28.6                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 60.0                                                                  C.sub..0.  = 300.0                        A cells = 4                                                                         B cells = 3                                                                         C cells = 1                                                                         Vmax % = 29.8                                                                         A.sub..0.  = 16.1                                                                  B.sub..0.  = 76.2                                                                  C.sub..0.  = 315.8                        A cells = 4                                                                         B cells = 3                                                                         C cells = 2                                                                         Vmax % = 40.9                                                                         A.sub..0.  = 7.2                                                                   B.sub..0.  = 96.2                                                                  C.sub..0.  = 260.7                        A cells = 4                                                                         B cells = 3                                                                         C cells = 3                                                                         Vmax % = 47.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 108.2                                                                 C.sub..0.  = 251.8                        A cells = 4                                                                         B cells = 4                                                                         C cells = 0                                                                         Vmax % = 33.0                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 4                                                                         B cells = 4                                                                         C cells = 1                                                                         Vmax % = 39.9                                                                         A.sub..0.  = 22.8                                                                  B.sub..0.  = 97.2                                                                  C.sub..0.  = 240.0                        A cells = 4                                                                         B cells = 4                                                                         C cells = 2                                                                         Vmax % = 46.2                                                                         A.sub..0.  = 15.5                                                                  B.sub..0.  = 104.5                                                                 C.sub..0.  = 240.0                        A cells = 4                                                                         B cells = 4                                                                         C cells = 3                                                                         Vmax % = 52.0                                                                         A.sub..0.  = 8.0                                                                   B.sub..0.  = 112.0                                                                 C.sub..0.  = 240.0                        A cells = 4                                                                         B cells = 4                                                                         C cells = 4                                                                         Vmax % = 57.1                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 5                                                                         B cells = 3                                                                         C cells = 2                                                                         Vmax % = 36.4                                                                         A.sub..0.  = 6.5                                                                   B.sub..0.  = 67.6                                                                  C.sub..0.  = 304.9                        A cells = 5                                                                         B cells = 3                                                                         C cells = 3                                                                         Vmax % = 49.4                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 93.6                                                                  C.sub..0.  = 266.4                        A cells = 5                                                                         B cells = 4                                                                         C cells = 1                                                                         Vmax % = 38.2                                                                         A.sub..0.  = 18.9                                                                  B.sub..0.  = 79.6                                                                  C.sub..0.  = 316.1                        A cells = 5                                                                         B cells = 4                                                                         C cells = 2                                                                         Vmax % = 49.3                                                                         A.sub..0.  = 11.6                                                                  B.sub..0.  = 93.9                                                                  C.sub..0.  = 262.1                        A cells = 5                                                                         B cells = 4                                                                         C cells = 3                                                                         Vmax % = 55.8                                                                         A.sub..0.  = 5.9                                                                   B.sub..0.  = 102.8                                                                 C.sub..0.  = 252.8                        A cells = 5                                                                         B cells = 4                                                                         C cells = 4                                                                         Vmax % = 61.5                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 111.3                                                                 C.sub..0.  = 248.7                        A cells = 5                                                                         B cells = 5                                                                         C cells = 0                                                                         Vmax % = 41.2                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 5                                                                         B cells = 5                                                                         C cells = 1                                                                         Vmax % = 48.2                                                                         A.sub..0.  = 24.3                                                                  B.sub..0.  = 95.7                                                                  C.sub..0.  = 240.0                        A cells = 5                                                                         B cells = 5                                                                         C cells = 2                                                                         Vmax % = 54.7                                                                         A.sub..0.  = 18.5                                                                  B.sub..0.  = 101.5                                                                 C.sub..0.  = 240.0                        A cells = 5                                                                         B cells = 5                                                                         C cells = 3                                                                         Vmax % = 60.8                                                                         A.sub..0.  = 12.5                                                                  B.sub..0.  = 107.5                                                                 C.sub..0.  = 240.0                        A cells = 5                                                                         B cells = 5                                                                         C cells = 4                                                                         Vmax % = 66.3                                                                         A.sub..0.  = 6.4                                                                   B.sub..0.  = 113.6                                                                 C.sub..0.  = 240.0                        A cells = 5                                                                         B cells = 5                                                                         C cells = 5                                                                         Vmax % = 71.4                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 6                                                                         B cells = 3                                                                         C cells = 3                                                                         Vmax % = 42.9                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 60.0                                                                  C.sub..0.  = 300.0                        A cells = 6                                                                         B cells = 4                                                                         C cells = 3                                                                         Vmax % = 57.7                                                                         A.sub..0.  = 4.8                                                                   B.sub..0.  = 91.2                                                                  C.sub..0.  = 268.4                        A cells = 6                                                                         B cells = 4                                                                         C cells = 4                                                                         Vmax % = 64.7                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 101.4                                                                 C.sub..0.  = 258.6                        A cells = 6                                                                         B cells = 5                                                                         C cells = 1                                                                         Vmax % = 47.2                                                                         A.sub..0.  = 20.5                                                                  B.sub..0.  = 82.4                                                                  C.sub..0.  = 311.3                        A cells = 6                                                                         B cells = 5                                                                         C cells = 2                                                                         Vmax % = 57.6                                                                         A.sub..0.  = 14.5                                                                  B.sub..0.  = 92.7                                                                  C.sub..0.  = 263.2                        A cells = 6                                                                         B cells = 5                                                                         C cells = 3                                                                         Vmax % = 64.4                                                                         A.sub..0.  = 9.8                                                                   B.sub..0.  = 99.8                                                                  C.sub..0.  = 253.6                        A cells = 6                                                                         B cells = 5                                                                         C cells = 4                                                                         Vmax % = 70.4                                                                         A.sub..0.  = 5.0                                                                   B.sub..0.  = 106.5                                                                 C.sub..0.  = 249.3                        A cells = 6                                                                         B cells = 5                                                                         C cells = 5                                                                         Vmax % = 75.9                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 113.1                                                                 C.sub..0.  = 246.9                        A cells = 6                                                                         B cells = 6                                                                         C cells = 0                                                                         Vmax % = 49.5                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 6                                                                         B cells = 6                                                                         C cells = 1                                                                         Vmax % = 56.5                                                                         A.sub..0.  = 25.2                                                                  B.sub..0.  = 94.8                                                                  C.sub..0.  = 240.0                        A cells = 6                                                                         B cells = 6                                                                         C cells = 2                                                                         Vmax % = 63.1                                                                         A.sub..0.  = 20.4                                                                  B.sub..0.  = 99.6                                                                  C.sub..0.  = 240.0                        A cells = 6                                                                         B cells = 6                                                                         C cells = 3                                                                         Vmax % = 69.3                                                                         A.sub..0.  = 15.5                                                                  B.sub..0.  = 104.5                                                                 C.sub..0.  = 240.0                        A cells = 6                                                                         B cells = 6                                                                         C cells = 4                                                                         Vmax % = 75.2                                                                         A.sub..0.  = 10.5                                                                  B.sub..0.  = 109.5                                                                 C.sub..0.  = 240.0                        A cells = 6                                                                         B cells = 6                                                                         C cells = 5                                                                         Vmax % = 80.7                                                                         A.sub..0.  = 5.4                                                                   B.sub..0.  = 114.6                                                                 C.sub..0.  = 240.0                        A cells = 6                                                                         B cells = 6                                                                         C cells = 6                                                                         Vmax % = 85.7                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 7                                                                         B cells = 4                                                                         C cells = 3                                                                         Vmax % = 52.2                                                                         A.sub..0.  = 4.6                                                                   B.sub..0.  = 68.0                                                                  C.sub..0.  = 299.9                        A cells = 7                                                                         B cells = 4                                                                         C cells = 4                                                                         Vmax % = 66.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 89.0                                                                  C.sub..0.  = 271.0                        A cells = 7                                                                         B cells = 5                                                                         C cells = 3                                                                         Vmax % = 66.0                                                                         A.sub..0.  = 8.2                                                                   B.sub..0.  = 90.0                                                                  C.sub..0.  = 270.0                        A cells = 7                                                                         B cells = 5                                                                         C cells = 4                                                                         Vmax % = 73.3                                                                         A.sub..0.  = 4.1                                                                   B.sub..0.  = 98.2                                                                  C.sub..0.  = 259.7                        A cells = 7                                                                         B cells = 5                                                                         C cells = 5                                                                         Vmax % = 79.5                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 105.6                                                                 C.sub..0.  = 254.4                        A cells = 7                                                                         B cells = 6                                                                         C cells = 1                                                                         Vmax % = 54.8                                                                         A.sub..0.  = 22.1                                                                  B.sub..0.  = 83.0                                                                  C.sub..0.  = 317.0                        A cells = 7                                                                         B cells = 6                                                                         C cells = 2                                                                         Vmax % = 65.9                                                                         A.sub..0.  = 16.6                                                                  B.sub..0.  = 92.0                                                                  C.sub..0.  = 264.0                        A cells = 7                                                                         B cells = 6                                                                         C cells = 3                                                                         Vmax % = 72.8                                                                         A.sub..0.  = 12.6                                                                  B.sub..0.  = 97.8                                                                  C.sub..0.  = 254.2                        A cells = 7                                                                         B cells = 6                                                                         C cells = 4                                                                         Vmax % = 79.1                                                                         A.sub..0.  = 8.6                                                                   B.sub..0.  = 103.3                                                                 C.sub..0.  = 249.8                        A cells = 7                                                                         B cells = 6                                                                         C cells = 5                                                                         Vmax % = 84.9                                                                         A.sub..0.  = 4.4                                                                   B.sub..0.  = 108.8                                                                 C.sub..0.  = 247.3                        A cells = 7                                                                         B cells = 6                                                                         C cells = 6                                                                         Vmax % = 90.2                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 114.3                                                                 C.sub..0.  = 245.7                        A cells = 7                                                                         B cells = 7                                                                         C cells = 0                                                                         Vmax % = 57.7                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 7                                                                         B cells = 7                                                                         C cells = 1                                                                         Vmax % = 64.7                                                                         A.sub..0.  = 25.9                                                                  B.sub..0.  = 94.1                                                                  C.sub..0.  = 240.0                        A cells = 7                                                                         B cells = 7                                                                         C cells = 2                                                                         Vmax % = 71.4                                                                         A.sub..0.  = 21.8                                                                  B.sub..0.  = 98.2                                                                  C.sub..0.  = 240.0                        A cells = 7                                                                         B cells = 7                                                                         C cells = 3                                                                         Vmax % = 77.8                                                                         A.sub..0.  = 17.6                                                                  B.sub..0.  = 102.4                                                                 C.sub..0.  = 240.0                        A cells = 7                                                                         B cells = 7                                                                         C cells = 4                                                                         Vmax % = 83.9                                                                         A.sub..0.  = 13.4                                                                  B.sub..0.  = 106.6                                                                 C.sub..0.  = 240.0                        A cells = 7                                                                         B cells = 7                                                                         C cells = 5                                                                         Vmax % = 89.6                                                                         A.sub..0.  = 9.1                                                                   B.sub..0.  = 110.9                                                                 C.sub..0.  = 240.0                        A cells = 7                                                                         B cells = 7                                                                         C cells = 6                                                                         Vmax % = 95.0                                                                         A.sub..0.  = 4.6                                                                   B.sub..0.  = 115.4                                                                 C.sub..0.  = 240.0                        A cells = 7                                                                         B cells = 7                                                                         C cells = 7                                                                         Vmax % = 100.0                                                                        A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        __________________________________________________________________________

                                      TABLE 7                                     __________________________________________________________________________    Original number of cells = 8                                                  __________________________________________________________________________    A cells = 1                                                                         B cells = 1                                                                         C cells = 0                                                                         Vmax % = 7.2                                                                          A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 1                                                                         B cells = 1                                                                         C cells = 1                                                                         Vmax % = 12.5                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 2                                                                         B cells = 1                                                                         C cells = 1                                                                         Vmax % = 12.5                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 60.0                                                                  C.sub..0.  = 300.0                        A cells = 2                                                                         B cells = 2                                                                         C cells = 0                                                                         Vmax % = 14.4                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 2                                                                         B cells = 2                                                                         C cells = 1                                                                         Vmax % = 20.2                                                                         A.sub..0.  = 15.5                                                                  B.sub..0.  = 104.5                                                                 C.sub..0.  = 240.0                        A cells = 2                                                                         B cells = 2                                                                         C cells = 2                                                                         Vmax % = 25.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 3                                                                         B cells = 2                                                                         C cells = 2                                                                         Vmax % = 28.3                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 101.4                                                                 C.sub..0.  = 258.6                        A cells = 3                                                                         B cells = 3                                                                         C cells = 0                                                                         Vmax % = 21.7                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 3                                                                         B cells = 3                                                                         C cells = 1                                                                         Vmax % = 27.6                                                                         A.sub..0.  = 20.4                                                                  B.sub..0.  = 99.6                                                                  C.sub..0.  = 240.0                        A cells = 3                                                                         B cells = 3                                                                         C cells = 2                                                                         Vmax % = 32.9                                                                         A.sub..0.  = 10.5                                                                  B.sub..0.  = 109.5                                                                 C.sub..0.  = 240.0                        A cells = 3                                                                         B cells = 3                                                                         C cells = 3                                                                         Vmax % = 37.5                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 4                                                                         B cells = 2                                                                         C cells = 2                                                                         Vmax % = 25.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 60.0                                                                  C.sub..0.  = 300.0                        A cells = 4                                                                         B cells = 3                                                                         C cells = 1                                                                         Vmax % = 26.1                                                                         A.sub..0.  = 16.1                                                                  B.sub..0.  = 76.2                                                                  C.sub..0.  = 315.8                        A cells = 4                                                                         B cells = 3                                                                         C cells = 2                                                                         Vmax % = 35.8                                                                         A.sub..0.  = 7.2                                                                   B.sub..0.  = 96.2                                                                  C.sub..0.  = 260.7                        A cells = 4                                                                         B cells = 3                                                                         C cells = 3                                                                         Vmax % = 41.1                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 108.2                                                                 C.sub..0.  = 251.8                        A cells = 4                                                                         B cells = 4                                                                         C cells = 0                                                                         Vmax % = 28.9                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 4                                                                         B cells = 4                                                                         C cells = 1                                                                         Vmax % = 34.9                                                                         A.sub..0.  = 22.8                                                                  B.sub..0.  = 97.2                                                                  C.sub..0.  = 240.0                        A cells = 4                                                                         B cells = 4                                                                         C cells = 2                                                                         Vmax % = 40.5                                                                         A.sub..0.  = 15.5                                                                  B.sub..0.  = 104.5                                                                 C.sub..0.  = 240.0                        A cells = 4                                                                         B cells = 4                                                                         C cells = 3                                                                         Vmax % = 45.5                                                                         A.sub..0.  = 8.0                                                                   B.sub..0.  = 112.0                                                                 C.sub..0.  = 240.0                        A cells = 4                                                                         B cells = 4                                                                         C cells = 4                                                                         Vmax % = 50.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 5                                                                         B cells = 3                                                                         C cells = 2                                                                         Vmax % = 31.9                                                                         A.sub..0.  = 6.5                                                                   B.sub..0.  = 67.6                                                                  C.sub..0.  = 304.9                        A cells = 5                                                                         B cells = 3                                                                         C cells = 3                                                                         Vmax % = 43.2                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 93.6                                                                  C.sub..0.  = 266.4                        A cells = 5                                                                         B cells = 4                                                                         C cells = 1                                                                         Vmax % = 33.4                                                                         A.sub..0.  = 18.9                                                                  B.sub..0.  = 79.6                                                                  C.sub..0.  = 316.1                        A cells = 5                                                                         B cells = 4                                                                         C cells = 2                                                                         Vmax % = 43.1                                                                         A.sub..0.  = 11.6                                                                  B.sub..0.  = 93.9                                                                  C.sub..0.  = 262.1                        A cells = 5                                                                         B cells = 4                                                                         C cells = 3                                                                         Vmax % = 48.8                                                                         A.sub..0.  = 5.9                                                                   B.sub..0.  = 102.8                                                                 C.sub..0.  = 252.8                        A cells = 5                                                                         B cells = 4                                                                         C cells = 4                                                                         Vmax % = 53.8                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 111.3                                                                 C.sub..0.  = 248.7                        A cells = 5                                                                         B cells = 5                                                                         C cells = 0                                                                         Vmax % = 36.1                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 5                                                                         B cells = 5                                                                         C cells = 1                                                                         Vmax % = 42.2                                                                         A.sub..0.  = 24.3                                                                  B.sub..0.  = 95.7                                                                  C.sub..0.  = 240.0                        A cells = 5                                                                         B cells = 5                                                                         C cells = 2                                                                         Vmax % = 47.9                                                                         A.sub..0.  = 18.5                                                                  B.sub..0.  = 101.5                                                                 C.sub..0.  = 240.0                        A cells = 5                                                                         B cells = 5                                                                         C cells = 3                                                                         Vmax % = 53.2                                                                         A.sub..0.  = 12.5                                                                  B.sub..0.  = 107.5                                                                 C.sub..0.  = 240.0                        A cells = 5                                                                         B cells = 5                                                                         C cells = 4                                                                         Vmax % = 58.0                                                                         A.sub..0.  = 6.4                                                                   B.sub..0.  = 113.6                                                                 C.sub..0.  = 240.0                        A cells = 5                                                                         B cells = 5                                                                         C cells = 5                                                                         Vmax % = 62.5                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 6                                                                         B cells = 3                                                                         C cells = 3                                                                         Vmax % = 37.5                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 60.0                                                                  C.sub..0.  = 300.0                        A cells = 6                                                                         B cells = 4                                                                         C cells = 3                                                                         Vmax % = 50.5                                                                         A.sub..0.  = 4.8                                                                   B.sub..0.  = 91.2                                                                  C.sub..0.  = 268.4                        A cells = 6                                                                         B cells = 4                                                                         C cells = 4                                                                         Vmax % = 56.6                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 101.4                                                                 C.sub..0.  = 258.6                        A cells = 6                                                                         B cells = 5                                                                         C cells = 1                                                                         Vmax % = 41.3                                                                         A.sub..0.  = 20.5                                                                  B.sub..0.  = 82.4                                                                  C.sub..0.  = 311.3                        A cells = 6                                                                         B cells = 5                                                                         C cells = 2                                                                         Vmax % = 50.4                                                                         A.sub..0.  = 14.5                                                                  B.sub..0.  = 92.7                                                                  C.sub..0.  = 263.2                        A cells = 6                                                                         B cells = 5                                                                         C cells = 3                                                                         Vmax % = 56.3                                                                         A.sub..0.  = 9.8                                                                   B.sub..0.  = 99.8                                                                  C.sub..0.  = 253.6                        A cells = 6                                                                         B cells = 5                                                                         C cells = 4                                                                         Vmax % = 61.6                                                                         A.sub..0.  = 5.0                                                                   B.sub..0.  = 106.5                                                                 C.sub..0.  = 249.3                        A cells = 6                                                                         B cells = 5                                                                         C cells = 5                                                                         Vmax % = 66.4                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 113.1                                                                 C.sub..0.  = 246.9                        A cells = 6                                                                         B cells = 6                                                                         C cells = 0                                                                         Vmax % = 43.3                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 6                                                                         B cells = 6                                                                         C cells = 1                                                                         Vmax % = 49.4                                                                         A.sub..0.  = 25.2                                                                  B.sub..0.  = 94.8                                                                  C.sub..0.  = 240.0                        A cells = 6                                                                         B cells = 6                                                                         C cells = 2                                                                         Vmax % = 55.2                                                                         A.sub..0.  = 20.4                                                                  B.sub..0.  = 99.6                                                                  C.sub..0.  = 240.0                        A cells = 6                                                                         B cells = 6                                                                         C cells = 3                                                                         Vmax % = 60.7                                                                         A.sub..0.  = 15.5                                                                  B.sub..0.  = 104.5                                                                 C.sub..0.  = 240.0                        A cells = 6                                                                         B cells = 6                                                                         C cells = 4                                                                         Vmax % = 65.8                                                                         A.sub..0.  = 10.5                                                                  B.sub..0.  = 109.5                                                                 C.sub..0.  = 240.0                        A cells = 6                                                                         B cells = 6                                                                         C cells = 5                                                                         Vmax % = 70.6                                                                         A.sub..0.  = 5.4                                                                   B.sub..0.  = 114.6                                                                 C.sub..0.  = 240.0                        A cells = 6                                                                         B cells = 6                                                                         C cells = 6                                                                         Vmax % = 75.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 7                                                                         B cells = 4                                                                         C cells = 3                                                                         Vmax % = 45.6                                                                         A.sub..0.  = 4.6                                                                   B.sub..0.  = 68.0                                                                  C.sub..0.  = 299.9                        A cells = 7                                                                         B cells = 4                                                                         C cells = 4                                                                         Vmax % = 57.7                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 89.0                                                                  C.sub..0.  = 271.0                        A cells = 7                                                                         B cells = 5                                                                         C cells = 3                                                                         Vmax % = 57.7                                                                         A.sub..0.  = 8.2                                                                   B.sub..0.  = 90.0                                                                  C.sub..0.  = 270.0                        A cells = 7                                                                         B cells = 5                                                                         C cells = 4                                                                         Vmax % = 64.1                                                                         A.sub..0.  = 4.1                                                                   B.sub..0.  = 98.2                                                                  C.sub..0.  = 259.7                        A cells = 7                                                                         B cells = 5                                                                         C cells = 5                                                                         Vmax % = 69.5                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 105.6                                                                 C.sub..0.  = 254.4                        A cells = 7                                                                         B cells = 6                                                                         C cells = 1                                                                         Vmax % = 47.9                                                                         A.sub..0.  = 22.1                                                                  B.sub..0.  = 83.0                                                                  C.sub..0.  = 317.0                        A cells = 7                                                                         B cells = 6                                                                         C cells = 2                                                                         Vmax % = 57.6                                                                         A.sub..0.  = 16.6                                                                  B.sub..0.  = 92.0                                                                  C.sub..0.  = 264.0                        A cells = 7                                                                         B cells = 6                                                                         C cells = 3                                                                         Vmax % = 63.7                                                                         A.sub..0.  = 12.6                                                                  B.sub..0.  = 97.8                                                                  C.sub..0.  = 254.2                        A cells = 7                                                                         B cells = 6                                                                         C cells = 4                                                                         Vmax % = 69.2                                                                         A.sub..0.  = 8.6                                                                   B.sub..0.  = 103.3                                                                 C.sub..0.  = 249.8                        A cells = 7                                                                         B cells = 6                                                                         C cells = 5                                                                         Vmax % = 74.3                                                                         A.sub..0.  = 4.4                                                                   B.sub..0.  = 108.8                                                                 C.sub..0.  = 247.3                        A cells = 7                                                                         B cells = 6                                                                         C cells = 6                                                                         Vmax % = 78.9                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 114.3                                                                 C.sub..0.  = 245.7                        A cells = 7                                                                         B cells = 7                                                                         C cells = 0                                                                         Vmax % = 50.5                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 7                                                                         B cells = 7                                                                         C cells = 1                                                                         Vmax % = 56.6                                                                         A.sub..0.  = 25.9                                                                  B.sub..0.  = 94.1                                                                  C.sub..0.  = 240.0                        A cells = 7                                                                         B cells = 7                                                                         C cells = 2                                                                         Vmax % = 62.5                                                                         A.sub..0.  = 21.8                                                                  B.sub..0.  = 98.2                                                                  C.sub..0.  = 240.0                        A cells = 7                                                                         B cells = 7                                                                         C cells = 3                                                                         Vmax % = 68.1                                                                         A.sub..0.  = 17.6                                                                  B.sub..0.  = 102.4                                                                 C.sub..0.  = 240.0                        A cells = 7                                                                         B cells = 7                                                                         C cells = 4                                                                         Vmax % = 73.4                                                                         A.sub..0.  = 13.4                                                                  B.sub..0.  = 106.6                                                                 C.sub..0.  = 240.0                        A cells = 7                                                                         B cells = 7                                                                         C cells = 5                                                                         Vmax % = 78.4                                                                         A.sub..0.  = 9.1                                                                   B.sub..0.  = 110.9                                                                 C.sub..0.  = 240.0                        A cells = 7                                                                         B cells = 7                                                                         C cells = 6                                                                         Vmax % = 83.1                                                                         A.sub..0.  = 4.6                                                                   B.sub..0.  = 115.4                                                                 C.sub..0.  = 240.0                        A cells = 7                                                                         B cells = 7                                                                         C cells = 7                                                                         Vmax % = 87.5                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        A cells = 8                                                                         B cells = 4                                                                         C cells = 4                                                                         Vmax % = 50.0                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 60.0                                                                  C.sub..0.  = 300.0                        A cells = 8                                                                         B cells = 5                                                                         C cells = 3                                                                         Vmax % = 50.7                                                                         A.sub..0.  = 8.2                                                                   B.sub..0.  = 68.4                                                                  C.sub..0.  = 307.8                        A cells = 8                                                                         B cells = 5                                                                         C cells = 4                                                                         Vmax % = 64.9                                                                         A.sub..0.  = 3.6                                                                   B.sub..0.  = 87.7                                                                  C.sub..0.  = 272.8                        A cells = 8                                                                         B cells = 6                                                                         C cells = 2                                                                         Vmax % = 52.1                                                                         A.sub..0.  = 16.1                                                                  B.sub..0.  = 76.2                                                                  C.sub..0.  = 315.8                        A cells = 8                                                                         B cells = 6                                                                         C cells = 3                                                                         Vmax % = 64.9                                                                         A.sub..0.  = 10.8                                                                  B.sub..0.  = 89.4                                                                  C.sub..0.  = 271.2                        A cells = 8                                                                         B cells = 6                                                                         C cells = 4                                                                         Vmax % = 71.5                                                                         A.sub..0.  = 7.2                                                                   B.sub..0.  = 96.2                                                                  C.sub..0.  = 260.7                        A cells = 8                                                                         B cells = 6                                                                         C cells = 5                                                                         Vmax % = 77.2                                                                         A.sub..0.  = 3.7                                                                   B.sub..0.  = 102.3                                                                 C.sub..0.  = 255.2                        A cells = 8                                                                         B cells = 6                                                                         C cells = 6                                                                         Vmax % = 82.3                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 108.2                                                                 C.sub..0.  = 251.8                        A cells = 8                                                                         B cells = 7                                                                         C cells = 1                                                                         Vmax % = 55.4                                                                         A.sub..0.  = 23.1                                                                  B.sub..0.  = 84.2                                                                  C.sub..0.  = 315.3                        A cells = 8                                                                         B cells = 7                                                                         C cells = 2                                                                         Vmax % = 64.9                                                                         A.sub..0.  = 18.2                                                                  B.sub..0.  = 91.5                                                                  C.sub..0.  = 264.7                        A cells = 8                                                                         B cells = 7                                                                         C cells = 3                                                                         Vmax % = 71.1                                                                         A.sub..0.  = 14.7                                                                  B.sub..0.  = 96.5                                                                  C.sub..0.  = 254.7                        A cells = 8                                                                         B cells = 7                                                                         C cells = 4                                                                         Vmax % = 76.7                                                                         A.sub..0.  = 11.2                                                                  B.sub..0.  = 101.2                                                                 C.sub..0.  = 250.2                        A cells = 8                                                                         B cells = 7                                                                         C cells = 5                                                                         Vmax % = 82.0                                                                         A.sub..0.  = 7.6                                                                   B.sub..0.  = 105.8                                                                 C.sub..0.  = 247.6                        A cells = 8                                                                         B cells = 7                                                                         C cells = 6                                                                         Vmax % = 86.9                                                                         A.sub..0.  = 3.9                                                                   B.sub..0.  = 110.4                                                                 C.sub..0.  = 246.0                        A cells = 8                                                                         B cells = 7                                                                         C cells = 7                                                                         Vmax % = 91.5                                                                         A.sub..0.  = 0.0                                                                   B.sub..0.  = 115.2                                                                 C.sub..0.  = 244.9                        A cells = 8                                                                         B cells = 8                                                                         C cells = 0                                                                         Vmax % = 57.7                                                                         A.sub..0.  = 30.0                                                                  B.sub..0.  = 90.0                                                                  C.sub..0.  = 272.3                        A cells = 8                                                                         B cells = 8                                                                         C cells = 2                                                                         Vmax % = 69.8                                                                         A.sub..0.  = 22.8                                                                  B.sub..0.  = 97.2                                                                  C.sub..0.  = 240.0                        A cells = 8                                                                         B cells = 8                                                                         C cells = 3                                                                         Vmax % = 75.5                                                                         A.sub..0.  = 19.2                                                                  B.sub..0.  = 100.8                                                                 C.sub..0.  = 240.0                        A cells = 8                                                                         B cells = 8                                                                         C cells = 4                                                                         Vmax % = 80.9                                                                         A.sub..0.  = 15.5                                                                  B.sub..0.  = 104.5                                                                 C.sub..0.  = 240.0                        A cells = 8                                                                         B cells = 8                                                                         C cells = 5                                                                         Vmax % = 86.1                                                                         A.sub..0.  = 11.8                                                                  B.sub..0.  = 108.2                                                                 C.sub..0.  = 240.0                        A cells = 8                                                                         B cells = 8                                                                         C cells = 6                                                                         Vmax % = 91.0                                                                         A.sub..0.  = 8.0                                                                   B.sub..0.  = 112.0                                                                 C.sub..0.  = 240.0                        A cells = 8                                                                         B cells = 8                                                                         C cells = 7                                                                         Vmax % = 95.7                                                                         A.sub..0.  = 4.1                                                                   B.sub..0.  = 115.9                                                                 C.sub..0.  = 240.0                        A cells = 8                                                                         B cells = 8                                                                         C cells = 8                                                                         Vmax % = 100.0                                                                        A.sub..0.  = 0.0                                                                   B.sub..0.  = 120.0                                                                 C.sub..0.  = 240.0                        __________________________________________________________________________

The angles given in Tables 1-7 give the optimum results, but the anglesmay be fairly difficult to calculate, especially when the number offunctional cells is different in all three phases. However, utilizingother teachings of this invention, it is not necessary to calculatethese angles. An existing control structure can be modified to implementa balanced bypass control, with results almost as good as Tables 1-7.Output voltage of the individual cells in each leg is controlled bypulse-width modulation. This modulation is implemented as shown in FIG.1c by comparing command waveforms for each phase or leg to a group oftriangular carrier waveforms. The carrier waveforms oscillate at thedesired switching frequency for the cells. These carrier waveforms havevarious phase angles to obtain harmonic cancellation between the cells.The command waveforms are simply replicas of the desired output voltagesfrom point N to points A, B and C, namely the individual legs A, B andC. When the array of cells is used to drive a load such as a motor, thedesired line-to-line output voltages are typically sinusoidal in nature.However, if sinusoidal command waveforms are employed, then the maximumavailable output voltage will be limited to the value where the sinewave amplitude becomes equal to the carrier amplitude. With three-phasesine waves, at the moment when one phase reaches maximum voltage, theother two phases are only at half of the maximum voltage with oppositepolarity. This results in unused capacity. To improve the maximumvoltage limit, a control method such as shown in FIG. 6 is often used.The original sinusoidal commands, VA*, VB*, VC*, are processed as shownin the block diagram of FIG. 6. Output of this process is then sent tothe pulse-width modulator.

Shown in FIG. 6 (prior art), a block labeled SELECT MAXIMUM produces asignal equal to the most positive of the three voltage commands at anyinstant. A similar block labeled SELECT MINIMUM produces a signal equalto the most negative of the three voltage commands at any instant. Thesetwo signals are added, and the sum is divided in half. The resultingsignal is then subtracted from each of the original voltage commands, toproduce a new set of voltage commands which are then sent to thepulse-width modulator. Modified voltage commands EA*, EB* and EC* arepeak-reduced commands that are sent to the PWM control. For example, ifthe magnitude of the most positive voltage command is equal to the mostnegative, the output of the sum will be zero. However, if the magnitudeof the most positive voltage command is greater than the most negative,the output of the sum will be positive. When half of this difference issubtracted from all three commands, the resulting new command set, EA*,EB*, EC*, will have most positive and most negative values of equalsize. As shown in FIG. 6, the peak voltage reduction method subtractsthe same signal from all three commands. Such a signal is called a"common mode signal." The polarity of the subtraction is always suchthat the command with the largest magnitude is reduced, while themagnitude of the one or both of the other commands is increased. Ineffect, the phases which have extra capacity are used to "help" thephase with the greatest burden. This methodology increases the availableline-to-line voltage by 20% over the sinusoidal case. It can also beused with the failed cell bypass invention, with a simple modification.

The peak voltage reduction method of FIG. 6 can be modified to alsoimplement the new bypass invention methodology. FIG. 7 shows a verysimple modification. The only change needed to the FIG. 6 diagram is tointroduce adjustable gains KA, KB and KC to the sinusoidal inputcommands VA*, VB* and VC*. These new gains are normally unity if nocells are bypassed. In that way they have no effect on the output valuesEA*, EB* and EC*. However, if one or more cells are bypassed, then thevalues of these gains for any phase, where the number of functionalcells has been reduced, is increased to the ratio of the normal cellcount divided by the actual unfailed cell count. The result is to tendto increase the command to the remaining cells by the amount needed tomaintain the original output voltage. Gain function blocks KA, KB and KCprovide this function. Since this new command is larger than thecommands to the other phases, which have lost fewer or no cells, acommon-mode signal is generated which then reduces the burden on theremaining cells and causes the cells in the other phase to "help" supplyvoltage to the phase or phases having legs with failed cells.

FIGS. 8, 9, and 10 show waveforms from FIG. 7 with zero, two, and fourcells bypassed, respectively. Shown in FIG. 8, the gains for therespective legs KA, KB, and KC, are equal to one, as no cells havefailed. In FIG. 7 the signals marked VA*, VB*, and VC* are the balancedsinusoidal voltage commands originating in other parts of the control.These signals are multiplied by gains KA, KB, and KC respectively togenerate signals UA*, UB*, and UC*. FIG. 8 shows the case of no cellsbypassed as in FIG. 2 (so that KA=1, KB=1, and KC=1); therefore in FIG.8a UA*, UB*, and UC* are also balanced sinusoidal voltages. Note that atthe instant when UB* reaches its peak positive value, both UA* and UC*are negative, but with only half the magnitude of UB*. FIG. 8b shows thesignal UMAX from the SELECT MAXIMUM block, and also the signal UMIN fromthe SELECT MINIMUM block. In FIG. 8b only UB* has been shown forclarity; both UA* and UC* have been omitted. It is clear that the UMAXsignal follows whichever of the signals UA*, UB* or UC* is the mostpositive, while the UMIN signal follows whichever of the signals UA*,UB* or UC* is the most negative. FIG. 8c is the same as 8b, with thesignal UCOM added. UCOM is the result of adding together UMAX and UMIN,and dividing by two. UCOM is the common-mode signal that will besubtracted from the three signals UA*, UB*, and UC*. FIG. 8d shows theresult of that subtraction, where EA*=UA*-UCOM, EB*=UB*-UCOM, andEC*=UC*-UCOM. Note that these three signals have lower peak values thanUB* (or UA* or UC*, which are not shown). At the instant when UB*reaches its peak positive value, EB* has a smaller positive value; andboth EA* and EC* are negative with the same magnitude as EB*. When EA*,EB*, and EC* are used to control the PWM modulation of the cells; theeffect at that instant will be to reduce the peak voltage magnituderequired from the B-phase cells by increasing the magnitude requiredfrom the A-phase and C-phase cells.

However, in FIG. 9 cells B4 and B5 have been bypassed. The waveforms inFIG. 9 correspond to the outputs from FIG. 7 with cells B4 and B5bypassed. FIG. 9 shows the same signals as FIG. 8 for the case of twocells bypassed in phase B (as in FIG. 3). The signals VA*, VB*, and VC*are still balanced, but the gain KB has been increased to equal theratio of the normal cell count divided by the remaining un-bypassed cellcount, which is 5/3=1.67. The other gains are unaffected, so that KA=1,KB=1.67, and KC=1. Therefore in FIG. 9a UA* and UC* are balancedsinusoidal voltages but UB* is much larger. FIG. 9b shows the signalUMAX from the SELECT MAXIMUM block, and also the signal UMIN from theSELECT MINIMUM block under these conditions (UA* and UC* have beenomitted for clarity). FIG. 9c is the same as 9b, with the signal UCOMadded. UCOM now contains a significant component of the UB* signal, dueto the unbalance. FIG. 9d shows the result of subtracting UCOM from UA*,UB* and UC* to get EA*, EB* and EC*. Note that these three signals havepeak values lower than UB*, and that they all have the same peak valuesat different moments within each cycle. At the instant when UB* reachesits peak positive value, EB* has a significantly smaller positive value;and both EA* and EC* are negative with the same magnitude as EB*. WhenEA*, EB*, and EC* are used to control the PWM modulation of the cells;the effect is that all the remaining cells will be required to producethe same peak voltage, even though phase B is missing two out of fivecells. If the drive output voltage is gradually increased, all 13remaining cells will reach their voltage limit simultaneously. This willoccur at about 85% of the voltage available when all 15 cells werefunctioning. However, if two cells had been bypassed in each phase (asshown in FIG. 4), the maximum available voltage would be only 60%.

The voltage diagram of the power circuit for such a bypass arrangementis shown in FIG. 5. Hence, in this example, two cells have been bypassedin leg B, the constant k_(A) has been increased from the previous valueof 1 to the current value of 1.67. This value may be calculated from thefollowing equation: ##EQU1##

The total number of the cells in the leg includes those that arebypassed and those that are not bypassed. As shown in the example, k_(A)=5/3 or 1.67. FIG. 10 shows the waveforms from FIG. 7, having commandoutputs to the pulse-width modulation control, EA*, EB* and EC*. In thisexample cells A₂, A₃, A₄ and A₅ have been bypassed. FIG. 10 shows thesame signals as FIG. 8 for the case of four cells bypassed in phase A.The signals VA*, VB*, and VC* are still balanced, but the gain KB hasbeen increased to equal the ratio of the normal cell count divided bythe remaining un-bypassed cell count, which is 5/1=5. The other gainsare unaffected, so that KA=5, KB=1, and KC=1. Therefore in FIG. 10a UB*and UC* are balanced sinusoidal voltages but UA* is much larger. FIG.10b shows the signal UMAX from the SELECT MAXIMUM block, and also thesignal UMIN from the SELECT MINIMUM block under these conditions (UB*and UC* have been omitted for clarity). FIG. 10c is the same as 10b,with the signal UCOM added. UCOM now contains a dominant component ofthe UA* signal, due to the unbalance. FIG. 10d shows the result ofsubtracting UCOM from UA*, UB* and UC* to get EA*, EB* and EC*. Notethat these three signals have peak values lower than UAB*, and that theyall have the same peak values at different moments within each cycle. Atthe instant when UA* reaches its peak positive value, EA* has asignificantly smaller positive value; and both EB* and EC* are negativewith the same magnitude as EA*. When EA*, EB*, and EC* are used tocontrol the PWM modulation of the cells; the effect is that all theremaining cells will be required to produce the same peak voltage, eventhough phase A is missing four out of five cells. If the drive outputvoltage is gradually increased, all 11 remaining cells will reach theirvoltage limit simultaneously. This will occur at about 67% of thevoltage available when all 15 cells were functioning. However, if fourcells had been bypassed in each, the maximum available voltage would beonly 20%.

This results in new gain constants to the input of FIG. 7. These newconstants are KA=5, KB=1 and KC=1. As previously discussed, since thereare no failures in leg B or leg C, the constant is unity. This isderived by the total number of cells in each leg divided by the numberof cells which are operational and have not been bypassed. In eachinstance with regard to legs B and C, the values are 5/5. However,because leg A has cells A2, A3, A4 and A5 bypassed, the value for k_(A)is equal to 5; the total number of cells in the leg, divided by thenumber of cells that are operational, namely 1. The result is theconstant k_(A) =5. Revising these values of kA, and kC, the circuit ofFIG. 11a can be operated with four power cells failed in a single legand still maintain balanced output voltage to motor terminals A, B andC. Seventy-three percent of the operational power cells or converters,namely A₁, B₁₋₅ and C₁₋₅ are providing power to the motor. In such anoperation if the practice of shunting or bypassing an equal number offunctional cells was utilized, the maximum output voltage would be 20%between motor terminals. However, utilizing the present invention, theoutput voltage between the terminals of the motor in a system havingfour failed cells in a single leg is equal to 67%.

FIG. 11 shows a circuit diagram which can be used to provide themodified pulse-width modulation signals EA*, EB* and EC*. Inputs V_(A)", V_(B) " and V_(C) " are fed through gain controls 81-83, whichrepresent the cell failure constants kA, kB and kC. The selectminimum-select maximum circuitry utilizes a diode bridge, having diodes84, 86 and 88 feeding the select maximum. Similarly, diodes 85, 87 and89 provide voltage feeds for the select minimum function. Voltagedivider circuits utilizing resistors 94 and 95 provide thedivision-by-two function. The voltage divided-by-two function is thenfed to summers 90, 91 and 92, along with the respective gain modifiedcontrol signal values.

The method of FIGS. 7 or 11 almost achieves the same output voltages asusing calculated angles from Tables 1-7, but it does introduce smallamounts of distortion which will often be acceptable. Since the methodof FIG. 7 is simple, with no feedback loops, it may be preferred in somecases.

FIG. 12 shows a block diagram of another control function to reduce thepeak voltage command, and also to implement the new strategy, which ismore complex than FIG. 7 but gives better results. This method requiresan internal feedback loop with integration, but it avoids the distortionof FIG. 7 and comes even closer to achieving the same output voltages asusing the calculated angles of Table 7.

The principle difference between FIG. 7 and FIG. 12 is that thecommon-mode signal UCOM is subtracted from the sinusoidal commands VA*,VB* and VC* before the adjustable gains KA, KB, and KC are applied. Thesubtraction occurs in the summation functions 201, 202, and 203, whilethe gains are applied in blocks 204, 205, and 206. As in FIG. 7, block207 SELECT MAXIMUM produces a signal UMAX equal to the most positiveinput signal, but these input signals are now the outputs UA*, UB* andUC*. Similarly, block 208 SELECT MINIMUM produces a signal UMIN equal tothe most negative input signal, but these input signals are again theoutputs UA*, UB*, and UC*.

The signals UMAX and UMIN are added in summation function 209, anddivided in half in block 210. In block 210 the signal is also divided byKmax, which is equal to the largest of the three gains KA, KB, or KC.Division by Kmax is needed for stability in digital implementations withsampling, but is not needed in analog implementations. The output ofblock 210 is integrated with respect to time in function 211 to producesignal UCOM.

During operation of the method of FIG. 12, suppose that the mostpositive signal UMAX exceeds the amplitude of the most negative signalUMIN; so that a small positive remnant emerges from block 209 to drivethe integrator 211 via gain block 210. This will cause the integratoroutput UCOM to become more positive over time. When this more positivesignal UCOM is subtracted from VA*, VB*, and VC* in 201, 202, and 203,it will cause signals UA*, UB*, and UC* to become more negative. Thisprocess will continue until UMAX and UMIN are equal but opposite, sothat the summation output 209 becomes zero. At this point the mostpositive and most negative signals are equal but opposite, as desired.

The method of FIG. 12 is slightly superior to FIG. 7 because it does notintroduce distortion and allows slightly higher output voltage. However,it is more complex due to the feedback path with integration. Feedbackis necessary because the common-mode signal UCOM is derived downstreamof the point where it is used. Therefore in many cases the method ofFIG. 7 will be preferred.

While many of the various embodiments discussed hereinto before haveutilized bypass functions such as described in Figure ID, it isunderstood that other arrangements may be utilized to transfer theoutputs from various operating cells. FIG. 13 shows one such transferswitch. In this diagrammatic representation a normal input at 301 can beconnected to the output 304 via switch arm 303. In the alternativeposition, 303 can connect the output 304 to an alternate input 302. ThisSPDT switching arrangement is well-known to those in the electricalarts. As shown the switch arm 33 is driven by a fluid-operated piston 35which can be supplied through a tube 36. In the preferred embodimentsthe fluid would be air and the tube 306 could be of a plastic,non-electrical conducting material. Such materials are readilyavailable. 308 shows a source of pressurized air. This could be acaptive reservoir or a compressor or other source of pressurized fluid.Electrical operation of solenoid valve 307 causes switch arm 303 tomove. In this arrangement a transfer switch is used in lieu of thebypass contactors shown in FIG. 1d. One of the advantages of such anarrangement is that the mechanical contactor can be mounted adjacent tothe high voltage connection areas and electrical isolation is maintainedby the non-conducting tube 306. As a result, all high voltage would bemaintained in the high voltage area. Electrically operated solenoidvalve 307 could be a two-position valve in which fluid from 308 iscommunicated to piston 305 in one position and fluid from operatingpiston 305 is exhausted to atmosphere and source 308 is cut off in thealternative position.

The use of a single-pole double-throw transfer switch provides forcontinuity in drives having a cell failure. In addition use of thesingle-pole double-throw transfer switch allows for the elimination ofthe bypass fuse needed in the single-throw bypass scheme. That fuse isneeded for the possibility that the cell bypass must be activated evenif the main IGBTs fail to block voltage from the bus. In the SPDTembodiment, the "break before make" actuation eliminates the possibilityof bypassing a faulted bridge and thus prevents the formation of aconductive plasma which might be the result of a total energy dischargeinto fuses or faulted IGBTs from the faulted cell. This condition mightcause additional power circuit failures.

FIG. 14 shows a transfer switch using a spring-loaded contact. In thiscase a pneumatic trip release device 311 is attached to a barricade 312.A non-conducting trip lever 313 connects the trip release mechanism tothe release lever 318. The switch arm 318 operates in the single-poledouble-throw mode between alternative normal output sources 316 and 317.Spring 315 biases the control arm into one of two positions. In theembodiment shown the spring 315 is pulling downward on the switch arm318. However, the downward movement of switch arm 318 is limited by thetrip lever 314. In this position 318 is in electrical conduction withthe normal source at 316. The trip release device may be a pneumaticdevice powered similar to that shown in and discussed at FIG. 13. Whenthe trip release device is activated the latching mechanism of 318 and314 disengage. As a result the switch arm 318 is moved to be inelectrical conduction with the alternate source 317. On the device shownwhich utilizes a trip release device mounted adjacent to the barrierpanel 312, it is also contemplated that the trip release device 311could be mounted in close proximity to the high voltage transfer switchmechanism. In such case then it would be desirable to use the plastictubing and remotely operated electrically activated solenoid valve ofFIG. 13 for control of the transfer switch. Also shown in FIG. 14 is anauxiliary contact 310. The auxiliary contact is optional and may beutilized to electrically determine whether the transfer switch has beenoperated. The transfer switch of FIG. 14 is released by the electricaldrive equipment by giving an electrical signal which either directly orthrough a pneumatic link causes the trip release device 311 to operate.311 may, for example, be a fluid operated piston. Once the device hasoperated to move from its normal source to its alternate source, thetransfer switch will remain in that position until switch arm 318 ismechanically moved backward causing the latch and lever 314, 318 toreengage. Under normal conditions both the transfer and the resetoperations would occur under zero current conditions. The transferswitch of FIG. 14 has been shown as being a spring operated releasedevice, such a transfer switch could also be mechanically orpneumatically operated to go between either pole of the SPDT switchunit.

FIG. 15 shows three cells A1, A2, and A3 operating in their normal modein series. Their normal input 324 would, for example, be the node of aWYE configuration. In operation, should any one of the cells A1, A2, orA3 fail, the appropriate transfer switch 321, 322, or 323 operates tofirst disconnect that power cell from the circuit. As the respectiveswitch arm of the transfer switches 321, 322 and 323 move to the otherposition, a series arrangement of the remaining operative cells iscreated.

While certain applications of the invention have been shown whichutilize the peak voltage reduction methodology, it is to be understoodthat other embodiments may utilize the invention to balance the outputvoltage between phases without utilizing the "peak-voltage reductionmethod", such as by using angles from Tables 1-7. In addition, whilesome of the circuitry has shown analog methods, it is to be understoodthat the invention may be accomplished utilizing the appropriatesoftware programming. Digital methods may be easily substituted for thecircuitry shown. In addition, while the method used as an example inthis specification has used pulse-width modulation, it is understoodthat other control techniques may be equally utilized in practicing thisinvention.

While the invention has been described in relationship to certainembodiments, it is to be understood that other embodiments created byothers are also included within the invention and are covered by theclaims.

We claim:
 1. A method of operating a multiphase power supply having aplurality of converter cells connected in series in each of a pluralityof legs each of said legs connected between a node and a respective lineand such supply having line-to-line voltage outputs between pairs ofsaid legs comprising:(a) detecting a failed cell in any of said legs;(b) forming a current path in any of said legs having at least onefailed cell by providing a bypass around each of said failed cell; and(c) controlling the cells in the legs of said power supply to maximizesaid line-to-line voltage outputs, and to keep all line-to-line voltageoutputs generally equal in magnitude.
 2. The method of claim 1 furthercomprising maintaining the line-to-line phase generally balanced.
 3. Themethod of claim 1 further comprising maintaining the line-to-linevoltage generally equal in magnitude by adjusting the leg-to-leg phaserelationship.
 4. The method of claim 3 wherein said adjusting comprisescalculating leg-to-leg phase angles to produce generally balanceline-to-line voltage.
 5. The method of claim 3 wherein said adjusting ofthe leg-to-leg phase angle is according to predetermined angles basedupon the number of failed cells in each of said legs.
 6. The method ofclaim 5 wherein said predetermined angles are obtained from tables ofvalues.
 7. The method of claim 1 further comprising increasing a commandsignal to each non-bypassed of said converter cells in a leg having atleast one failed cell.
 8. The method of claim 7 wherein said increasingof said command signal is an amount generally equal to the ratio of thetotal number of cells in said leg to the number of non-bypassed cells insaid leg.
 9. The method of claim 1 further wherein said controllingfurther comprises increasing the magnitude of the output during aportion of the cycle of non-bypassed cells in each of said leg having atleast one failed cell.
 10. The method of claim 1 wherein saidcontrolling further comprises increasing the magnitude of the outputduring a portion of the cycle of non-bypassed cells in each of said leghaving no failed cells.
 11. The method of claim 10 wherein saidcontrolling further comprises increasing the magnitude of the outputduring a portion of the cycle of non-bypassed cells in each of said leghaving at least one failed cell.
 12. The method of claim 1 furthercomprising reducing the peak voltage demands between legs.
 13. Themethod of claim 1 further comprising pulse width modulating saidconverter cells with a command signal.
 14. The method of claim 1 furthercomprising generating voltage commands to provide peak voltage reductionand modifying such commands in response to detecting at least one failedcell.
 15. The method of claim 14 wherein said modifying furthercomprises increasing said commands by amount generally equal to theratio of the total number of cells in one of said legs to the number ofnon-bypassed cells in said one of said legs.
 16. A method of operating amultiphase power supply having a plurality of converter cells connectedin series in each of a plurality of legs each of said legs connectedbetween a node and a respective line and such supply having line-to-linevoltage outputs between pairs of said legs comprising:(a) detecting afailed cell in any of said legs; (b) forming a current path in any ofsaid legs having at least one failed cell by providing a transfer of atleast one of the input and output of each of said failed cells; and (c)controlling the cells in the legs of said power supply to maximize saidline-to-line voltage outputs, and to keep all line-to-line voltageoutputs generally equal in magnitude.
 17. The method of claim 16 furthercomprising maintaining the line-to-line phase voltages generallybalanced.
 18. The method of claim 16 further comprising maintaining theline-to-line voltage generally equal in magnitude by adjusting theleg-to-leg phase relationship.
 19. The method of claim 18 wherein saidadjusting comprises calculating leg-to-leg phase angles to producegenerally balance line-to-line voltage.
 20. The method of claim 18wherein said adjusting of the leg-to-leg phase angle is according topredetermined angles based upon the number of failed cells in each ofsaid legs.
 21. the method of claim 20 wherein said predetermined anglesare obtained from tables of values.
 22. The method of claim 16 furthercomprising increasing a command signal to each non-bypassed of saidconverter cells in a leg having at least one failed cell.
 23. The methodof claim 22 wherein said increasing of said command signal is an amountgenerally equal to the ratio of the total number of cells in said leg tothe number of non-bypassed cells in said leg.
 24. The method of claim 16further wherein said controlling further comprises increasing themagnitude of the output during a portion of the cycle of non-bypassedcells in each of said leg having at least one failed cell.
 25. Themethod of claim 16 wherein said controlling further comprises increasingthe magnitude of the output during a portion of the cycle ofnon-bypassed cells in each of said leg having no failed cells.
 26. Themethod of claim 25 wherein said controlling further comprises increasingthe magnitude of the output during a portion of the cycle ofnon-bypassed cells in each of said leg having at least one failed cell.27. The method of claim 16 further comprising reducing the peak voltagedemands between legs.
 28. The method of claim 16 further comprisinggenerating voltage commands to provide peak voltage reduction andmodifying such commands in response to detecting at least one failedcell.
 29. The method of claim 28 wherein said modifying furthercomprises increasing said commands by amount generally equal to theratio of the total number of cells in one of said legs to the number ofnon-bypassed cells in said one of said legs.
 30. The method of claim 16further comprising pulse width modulating said converter cells with acommand signal.
 31. The method of claim 16 wherein said transfer ispneumatically performed.
 32. The method of claim 31 wherein saidtransfer is through operations of a SPDT transfer switch.
 33. The methodof claim 32 wherein said operation of said transfer switch is through asource of pressurized fluid remotely located from said SPDT switchcontacts and pneumatically connected by a non-electrically conductingtube.
 34. The method of claim 33 wherein said source of pressurizedfluid is activated by an electrical signal.
 35. The method of claim 34further comprising generating said source with an electrically drivencompressor.
 36. A multiphase power supply having a line-to-line voltageoutput comprising:(a) a plurality of converter cells in seriesarrangement in each of a plurality of legs each of legs connectedbetween a node and a respective line; (b) a controller to control theoutput voltage of each of said cells thereby supplying said line-to-linevoltage output between pairs of said legs; (c) said controller detectinga failed cell in any of said legs and in response thereto removing saidfailed cell from said series arrangement; (d) said controllercontrolling said cell outputs to maximize said line-to-line voltageoutput and to keep all line-to-line voltage outputs generally equal inmagnitude.
 37. The multiphase power supply of claim 36 wherein saidcontroller maintains the line-to-line phase voltages generally balancedby controlling the output of operable cells.
 38. The multiphase powersupply of claim 36 wherein said controller maintains the line-to-linevoltage generally equal in magnitude by adjusting the leg-to-leg phaserelationship.
 39. The multiphase power supply of claim 36 furthercomprising said controller operating said cells having reduced peakvoltage demands.
 40. The multiphase power supply of claim 39 furthercomprising said controller generates voltage commands to provide peakvoltage reduction and modifies such commands in response to detection ofat least one failed cell.
 41. The multiphase power supply of claim 36wherein said controller adjusts the leg-to-leg phase angle according toa table of predetermined angles based upon the number of failed cells ineach of said legs.
 42. The multiphase power supply of claim 36 whereinsaid controller increases the magnitude of cell output during a portionof a cycle of operative cells in each of said leg having no failedcells.
 43. The multiphase power supply of claim 36 wherein saidcontroller operates a bypass to remove said failed cell from said seriesarrangement.
 44. The multiphase power supply of claim 36 wherein saidcontroller operates a transfer switch to remove said failed cell fromsaid series arrangement.
 45. The multiphase power supply of claim 44wherein said transfer switch is fluid operated.
 46. The multiphase powersupply of claim 45 wherein said transfer switch is operatedpneumatically from a fluid source remote from high voltage adjacent saidtransfer switch.
 47. The multiphase power supply of claim 45 whereinsaid fluid source includes a compressor and pneumatic pressure isconveyed to said transfer switch by an electrically non-conducting tube.